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

18d

#### 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,...
more

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...
more

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...
more

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...
more

#### 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...
more

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...
more

Derivative Calculus

05/06/21

#### Derivative Equations

Derivative Calculus

05/06/21

#### Derivative Equations

05/03/21

#### 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.

## Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.

Most questions answered within 4 hours.

#### OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.