356 Answered Questions for the topic Derivatives

11/04/14

Finding f'(c) With an Inequality
Suppose that f'(x)≤2 for 2≤x≤4. Show that f(4)-f(2)≤4. Assume that f does satisfy the conditions of the Mean Value Thereom on the interval [2,4].  I'm using f(b)-f(a)/b-a=f'(c). So I'm assuming... more
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11/03/14

How to find extremes on an open interval
The function V(x)=x(10-2x)(16-2x) on the interval 0<x<5 models the volume of a box.  Find the extreme values of V and interpret those values in terms of the volume of the box. I'm basically... more
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Derivatives Math Calculus

10/30/14

Find the equation of the tangent line to (y=ln x) at x=1
Find the equation of the tangent line to (y=ln x) at x=1 (a) Use it to calculate approximate values for ln(1.1) and ln(2). c. Using a graph, explain whether the approximate values are smaller or... more
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Derivatives Math Calculus Chain Rule

10/30/14

let h(x)=f(g(x)). Find: (a) h'1 (b) h'(2) (c) h'(3)
Need help   let h(x)=f(g(x)). Find: (a) h'1 (b) h'(2) (c) h'(3)
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Derivatives

10/27/14

find the derivative
find the derivative 1.f(x)= 2x-7/3x-2   2. f(x)=(8x-9)^-4   3.d/dx-(^8 square rtt 8x^7-10)   4.find dy/dx for y=ln(2x^3-x^2)
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10/26/14

find the derivative of....
y=(x)/(x2-4)1/2   i get y'=-4/(x2-4)3/2
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Derivatives Chain Rule

10/24/14

third derivative
f(x) = ln(ln(7x)) = f'''(x) = ?
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Derivatives Calculus

10/22/14

higher derivative
f(x) = x-1÷x+1 find the f(X)n
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10/21/14

What is the derivative of f (f^-1 (x))=x ?
Please show work
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10/21/14

Calculus Question: Tangents on Polar Coordinate of Polar Curve r=cos(theta)+sin(theta)
How do I find the polar coordinates of the points on the polar curve r=cos(theta)+sin(theta), 0(greater than or equal to)(theta)(less than or equal to)(pi), where the tangent line is horizontal or... more
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10/15/14

proving f'(x)/f(x)= 1/(x-a)
I couldn't understand and sole this question. please help    Define f(x):= (x-a1)(x-a2)(x-a3)... (x-at), where an are constants, 1≤n≤t , where t is some finite natural number. Show that... more
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10/12/14

Calculus Volume Decrease Question
If a snowball melts so that its surface area decreases at a rate of 1 cm^2/min, find the rate at which the diameter decreases when the diameter is 10 cm.
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10/12/14

Mean Value Theorem Help!
Verify the function f(x)=1/x satisfies the hypothesis of the mean value theorem on [1,3]. Then find all numbers c that satisfy the conclusion of the mean value theorem.
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10/07/14

Using derivatives and related rates in calculus?
"Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west at 20 mi/h. At what rate is the distance between the cars increasing two hours later?"   This... more
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Derivatives Calculus

09/24/14

Let f(x) = |x - 2| + 1/2 .
Let f(x) = |x - 2| + 1/2 .1.Find f '(1) and f '(3).2.Show that f '(2) does not exist. (Hint: use the definition ofderivatives.)   please show the steps to how you achieved the answer. 
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Derivatives

05/13/14

find the derivative of f
f(x)=x2-4x+3
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Derivatives

05/10/14

derivation of sin(3x)/(1+x^2)
sin3x/(1+x^2)
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04/24/14

Differentiation Rules for Exponential Functions
how do you find the second derivative of y=e-x^2
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04/23/14

Please help set up a derivative problem for business calc.
Suppose the annual cost per active-duty armed service member in a certain country increased from $80,000 in 1995 to $90,000 in 2000. In 1990, there were 2 million armed service personnel and this... more
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04/12/14

Applications of Sinusoidal Functions and Their Derivatives
A differential equation is an equation involving a function and one or more of its derivatives. Determine whether the function y=πsinθ+2πcosθ is a solution to the differential equation d^2y/dθ^2 +... more
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Derivatives Calculus Area Circles

04/01/14

Optimization Problems
A piece of plexiglass is in the shape of a semicircle with radius 2 m. Determine the dimensions of the rectangle with the greatest area that can be cut from the piece of plexiglass. 
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Derivatives

03/18/14

Derivative of a Polynomial Function
 Air is being pumped into a spherical balloon. The volume, V, in cubic centimetres, of the balloon is V=4/3πr^3, where the radius, r, is in centimetres.    a) Determine the instantaneous rate of... more
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Derivatives Derivative Proof

03/18/14

Derivative of a Polynomial Function
Show that there is no polynomial function that has a derivative of x^-1.
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03/18/14

Derivative of a Polynomial Function
Determine equations for the tangents to the cubic function y=2x^3 -3x^2 -11x +8 at the point where y=2.
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Derivatives

03/18/14

Derivative of a Polynomial Function
Determine equations for two lines that pass through the point (1,-5) and are tangent to the graph of y=x^2-2.
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