432 Answered Questions for the topic Derivative
Optimization word problem
A rectangular page is to contains 99 square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used.larger value = ?smaller...
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08/08/21
Optimization word problem
A farmer plans to enclose a rectangular pasture adjacent to a river. (see figure). The pasture must contain 320,000 square meters in order to provide enough grass for the herd. What dimensions will...
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08/07/21
Optimization question; fencing problem
A rancher has 560 feet of fencing with which to enclose two adjacent rectangular corrals (see figure). What dimensions should be used so that the enclosed area will be a maximum?x = ?y = ?any...
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08/07/21
Optimization problem
Find two positive numbers that satisfy the given requirements.The second number is the reciprocal of the first number and the sum is a minimum.first number=?second number=?any guidance will be much...
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08/07/21
Optimization question
Find two positive numbers satisfying the given requirements.The sum of the first and twice the second is 200 and the product is a maximumfirst number=?second number=?
(Falling ladder question); A ladder 25 ft long is leaning against a wall. The base of the ladder is pulled away from wall at rate of 2ft/sec.
A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second.(a) What is the velocity of the top of the ladder...
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finding population, with derivatives.
A population of 460 bacteria is introduced into a culture and grows in number according to the equation below, where t is measured in hours. Find the rate at which the population is growing...
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07/17/21
Let f(x) = 1/(1-x). Find a cubic polynomial p(x) so that f(0) = p(0), f'(0)=p'(0), f"(0)=p"(0), f'''(0)=p'''(0)
Please show working...Consider if f were a more complicated function. How would this be more efficient to finding values of f?Thank you!!
06/23/21
What's the quotient rule in words?
Question related to the mean value theorem and increasing and decreasing functions
Let L be a differentiable function on (0, ∞) such that L'(x)=1/x and L(1) = 0. Prove that for any two positive numbers a and b, L(ab) = L(a) + L(b). HINT: Begin by showing that, for any x > 0,...
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06/18/21
Limits, Derivative, Slope of Tangent and Equation of Tangent of a function
Consider the function f(x)= 1÷ x+3
Use the limit definition of the derivative to find the derivative of the function.
Find the slope of the tangent to f(x) at x=0
Find the equation of the tangent...
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06/17/21
Find the equation of the tangent line
Find the equation of the tangent line to the graph of the equation at the given point:ln(10 - y2) + 16 = -2x3 at (-2, 3)
06/08/21
On a given interval, if the antiderivative of f exists, is it unique? Why or why not? (You may cite theorems to support your answer.)
The question basically asks for a specific given interval, if the antiderivative of f exists, is it unique?If yes, why?If no, why not?In stating the reasons you can use specific theorems that would...
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06/07/21
Refer to the description below. Are there any other anti-derivatives of f(x) = 12x^2 + 2x, and g(x) = cos x. (Cite another anti-derivative for each function.)
There are already two known antiderivatives of each function, specifically:1.) f(x) = 12x^2 + 2x:Antiderivatives:4x3+x24x3+x2-12.) g(x)=cos xAntiderivatives:sin xsin x+πNow, what are the other...
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Calculus Problem
The demand for thousands of "Zombie Death Bats" (patent pending) is given by D(p) = 124*exp(-0.0023*p), where p is the price in dollars.At what price should the "Zombie Death Bats" be sold to...
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Derivative Calculus
05/25/21
Need help with a Calculus question.
For what value(s) of x does the graph of the function f(x)=x+2 cos x have a horizontal tangent line? Justify your answer analytically (that is, without the use of graphing software)
Derivative Calculus
05/19/21
Find the equation of the normal line for f(x)= x+ (1/x) at the point x=2 in slope point form
Let f(4) = 3 and f'(4) = 2. If g(x) = ( x f(x^2) ) / (x^2 + 1), then g'(2) = ?
https://imgur.com/a/f3j9HkBLet f(4) = 3 and f'(4) = 2. If g(x) = ( x f(x2) ) / (x2 + 1), then g'(2) = ?
Derivative Calculus
05/13/21
Find the equation of the normal line to the function y=3x+sin3x at point (0,0)
05/10/21
How do I solve this Derivation Proof in Logic ¬A → [(B ∧ A) → C]?
I have attempted to solve this question multiple times but keep getting it wrong. Im only allowed to use Conjunction Introduction/Elimination, Conditional Introduction/Elimination, Negation...
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Derivative Calculus
05/06/21
Derivative Equations
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