325 Answered Questions for the topic Derivative
(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... more
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... more
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!!
Differentiate (v^3+5v^2)(2v^7-6v^5) with respect to v.
Differentiate 2c to the fifteenth power with respect to c.
A triangle is bounded by the lines y=0, y=2x and y=-x/2+k, where k is positive. Find the value of k knowing that the area of the triangle is 80
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,... more
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... more
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)
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... more
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... more
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... more
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)
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) = ?
Find the equation of the normal line to the function y=3x+sin3x at point (0,0)
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... more
Find f’(2) for f(x)= 1/x-3 using the definition of the derivative
Consider the function, f(x) = √x-4 (square root goes over x-4) at the point (8,2) find the slope of the tangent line to the curve using the definition of the derivative
And find the equation of the tangent line. I am confused on how to treat the square root as I haven’t covered a question using them like this yet.