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Calculus

11/01/23

Mean Value Theorem

Suppose that f(0) = 3 and f'(x) < 4 for all values of x. Use the Mean Value Theorem to determine how large f(4) can possibly be. Answer: f(4) < 3

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Calculus

11/01/23

let f(x) = x sqrt x+7 . Answer the following questions Find the average slope of the function f on the interval [ -7,0] . Average slope = Verifty the Mean Value Theorem by finding a number c in (... more

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Calculus

11/01/23

Derivative Question

Find dy/dx of y = sqrt(1+sin sqrt(x))

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Calculus Math

11/01/23

Derivatives and Shape of Graph

Consider the function q(t)=e^t/(3+e^t)interval(s) on which q is increasing:interval(s) on which q is decreasing:point(s) at which q achieves a local maximum:point(s) at which q achieves a local... more

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Calculus Math

11/01/23

Derivatives and Shape of Graph

Let f(x)=6√xe^-x for x>0. Fill in the values or intervals below.interval(s) on which f is increasing:interval(s) on which f is decreasing:point(s) at which f achieves a local maximum:point(s) at... more

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Calculus Math

11/01/23

Derivatives and Shape of Graph

Let h(t)=(2t^2)/(t^2+3). Fill in the values or intervals below.interval(s) on which h is increasing:interval(s) on which h is decreasing:point(s) at which h achieves a local maximum:point(s) at... more

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Calculus Math

11/01/23

Derivatives and Shape of Graph

Let p(z) = 5z^4-10z^2+15. Find the values or intervals below.interval(s) on which p is increasing:interval(s) on which p is decreasing:point(s) at which p achieves a local maximum:point(s) at which... more

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Calculus

10/31/23

Linear Approximation and Differentials

The side length of a cube is measured to be x = 1.3 feet, with an error of at most 1 inch. (A) (No calculus) Determine the difference, in ft^3, between the volume of the cubecomputed with the... more

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Calculus

10/31/23

Determine all intervals which contain a number c satisfying h''(c) = 2

consider a function h that is twice differentiable. This means that h is differentiable and its derivative,h' , is also differentiable. Some values of h'(x) are given in the table below x -8 -6... more

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Calculus

10/31/23

Evaluate the limit using L'Hospital's Rule lim┬(x→∞)⁡〖(7x)^(-1) e^3x 〗

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Calculus

10/31/23

Compute the requested derivative. Do not simplify your answer after applying the differentiation rules.

b) y=(x-3)/(x+4); Find d2y/dx2 c) y3+x3-5x(y-1)=2; Find dy/dx at (1,1)For b, I tried to do implicit differentiation by first using the quotient rule on d2y/dx2, but I got stuck there.For c, I got... more

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Calculus

10/31/23

Calculus BC - Optimization

Find the dimensions of a cylinder with volume of 12π and minimal surface area.

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Calculus

10/31/23

let f(x) = 5xˆ2. Determine the value of x such that the average rate of change of f(x) from 3 to x is 55

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Calculus

10/31/23

Evaluate the following limit: the limit as θ approaches 0, of sin(3θ)/(θ^2-2θ). DO NOT USE L'HOSPITAL'S RULE

The limit as θ approaches 0, of sin(3θ)/θ2-2θ. Without using L'Hospital's rule.After applying the derivative using the quotient rule, I got (3cos(3θ))(θ2-2θ)-(2θ-2)(sin(3θ))/(θ2-2θ)2Do I distribute... more

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Calculus

10/30/23

When the base is 3 feet from the wall, how fast is the bottom of the ladder moving away from the wall?

A 5 foot ladder is sliding down a wall with the top of the ladder moving down the wall at the rate of 1/2 foot per second. When the base is 3 feet from the wall, how fast is the bottom of the... more

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Calculus Precalculus

10/30/23

How to remember the unit circle?

If you are enrolled in a Pre-Calculus or Calculus Course your must remember the Unit Circle. In this video, I will show you how to never forget the unit circle in just 5 minutes.

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Calculus

10/30/23

absolute maximum

Consider the function f(x) = x^3e^6x -2< x< 2 The absolute maximum value is ... and this occurs at x equals ..... The absolute minimum value is .... and this occurs at x equals .

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Calculus

10/30/23

Absolute Min and Max

find the absolute maximum and absolute minimum values of f(x)=x-ln x on the interval [ 1/4,4] Find the absolute maximum of f on the interval Find the absolute minimum of f on the interval

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Calculus

10/30/23

absolute minimum and maximum

f(x) = 2x^3+18x^2-162x+11 with -9< x< 4This function has an absolute minimum the point ... and an absolute maximum at the point ... note : both parts of this answer should be entered as an... more

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Calculus

10/30/23

Linear approximation

Use linear approximation, i.e the tangent line, to approximate cube root 8.02 as follows. Let f(x)=cube root x and find the equation of the tangent line to f(x) at x=8 in the form y=mx+b.m =b=using... more

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Calculus

10/30/23

Linear approximation

Use linear approximation, i.e the tangent line, to approximate 3sqrt 8.02 as follows. Let f(x)=3sqrtx and find the equation of the tangent line to f(x) at x=8 in the form y=mx+b. m = b= using these... more

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Calculus

10/29/23

Find the linear approximation to the function f at the given point and then estimate. f(x,y) = sqrt(x^2 + y^2), (3,-4); estimate f(3.06,-3.92)

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Calculus

10/29/23

Lagrange Multipliers | Optimization between a 4th dimensional object and a 3rd dimensional object

Use lagrange multipliers to find the absolute maximum and minimum of for f(x,y,z)=8x-9y+7z and x^2+y^2+z^2=194

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Calculus

10/27/23

Right circular cone

Gravel is being dumped from a conveyor belt at a rate of 40 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast... more

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Calculus Math

10/27/23

Optimization problem

A box with a square base and an open top will be made from 1400 cm^2 of material.Find the largest possible volume of the box.Volume=???

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Mean Value Theorem

average slope find

Derivative Question

Derivatives and Shape of Graph

Derivatives and Shape of Graph

Derivatives and Shape of Graph

Derivatives and Shape of Graph

Linear Approximation and Differentials

Determine all intervals which contain a number c satisfying h''(c) = 2

Evaluate the limit using L'Hospital's Rule lim┬(x→∞)⁡〖(7x)^(-1) e^3x 〗

Compute the requested derivative. Do not simplify your answer after applying the differentiation rules.

Calculus BC - Optimization

let f(x) = 5xˆ2. Determine the value of x such that the average rate of change of f(x) from 3 to x is 55

Evaluate the following limit: the limit as θ approaches 0, of sin(3θ)/(θ^2-2θ). DO NOT USE L'HOSPITAL'S RULE

When the base is 3 feet from the wall, how fast is the bottom of the ladder moving away from the wall?

How to remember the unit circle?

absolute maximum

Absolute Min and Max

absolute minimum and maximum

Linear approximation

Linear approximation

Find the linear approximation to the function f at the given point and then estimate. f(x,y) = sqrt(x^2 + y^2), (3,-4); estimate f(3.06,-3.92)

Lagrange Multipliers | Optimization between a 4th dimensional object and a 3rd dimensional object

Right circular cone

Optimization problem

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