Calculus Answers

The derivative of f is x^3(x+5)(x-1). At which values of x will the graph of f have a relative maximum? A relative minimum?

Let f be the function given by f(x)=-x^2/3. Which of the following statements about f are true?

I. f is continuous at x=0.

II. f is differentiable at x=0;

III. f has an absolute maximum at x=0

apply intermedaite value theorem on x^5-x^3+3x-5

Can the intermediate value theorem can be applied to show the that there is a root of equation x^5-x^3+3x-5 in the given interval [1,2] if yes, apply it

The graph of every function from [0,1] to R is infinite. True or False

 Eliminate a & b from az+b=a²x+y

Expand e

ax cos bx by Maclaurins theorem. Hence prove that

e

x cos α

cos(x sin α) = 1 + x cos α +

x

2

2!

cos 2α +

x

3

3!

cos 3α + ⋯ ...

Instructions:Sketch the Graph of the following functions. Use a graphing paper in portrait orientation.

Show complete solution on the upper half of the graphing paper and the graph on the lower half portion. One function is the one graphing paper.

1.f(x)=2 sin (x-​π/​4)

2.f(x)=sin (x+π/​3)

3.f(x)=3 cos (x+π/​6)

4.f(x)=2 cos (x-2π)

5.f(x)=tan x

At the point (1,2) on the curve 4x²+2xy+y²=2 dy/dx = ? and d²y/dx² = ?