List each step by step and why these steps were taken.

List each step by step and why these steps were taken.

In Calculus, are any number to the power of x treated as E^x when working with derivatives? (i.e. 10^x ... 10xln(10)

Question 1 Find the value of k such that x = 2 is a critical number of f(x) =14x4−3x2+kx.

The marginal cost of producing the xth item is given by (-x+10)^2 Find the total cost function, C, assuming the total cost is zero if no items are produced. C(x)=...

The curve below has a horizontal tangent line at the point ( - 2 , 8 ) and at one other point. Find the coordinates of the second point where the curve has a horizontal tangent line. 16x^2+64x+25y^2-200y=-64 x-coordinate...

prove the identity arcsin [(x-1)/(x+1)] = 2 arctan √x - (pi/2)

if f'(x)=c (c a constant) for all x, use F(x)=f(x)-g(x) to show that f(x)=cx+d for some constant d

A. suppose that 3≤f'(x)≤5 for all values of x. show that 18≤f(8)-f(2)≤30 B. show that sin x < x if 0<x<2pi

a. show that a polynomial of degree 3 has at most three real roots b. show that a polynomial of degree n has at most n real roots.

A farmer finds that if she plants 95 trees per acre, each tree will yield 55 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by...

Find Absolute maximum and minimum values of each function over the indicated interval, and indicate the x-values at which they occur. f(x)=x^3-x^2-8x+8 ;[-2,0]

Give each step in order and tell why each step was taken to get the answer. g(x)=sqrt of x.

List why it is true or false and give each step, also include why each step was taken.

List each step by step and explain why each step was take.

Find the function of the form f(x)=a+bcos(cx) that is tangent to the line y=1 at the point (0,1), and tangent to the line y = x + (3/2) - (pi/4) at the point (pi/4, 3/2).

y=(xy)x Write an expression for dy/dx

Given the function h: |x − 1| < 0.2 =⇒ |h(x) − 4| < 1. a) Can you guarantee that there exists δ > 0 such that |x − 1| < δ =⇒ |h(x) − 4| < 0.5? If the answer is yes, provide one...

a paper cup as the shape of a cone with height 10 cm and radium 3 cm at the top. if water is poured into the cup at a rate of 2cm^3/s, how fast is the water level rising when water is 5 cm deep

function C(t)=K[(e^-at) - (e^-bt)], where a,b snd K are positive constants and b>a, is used to model the concentration at time t of a drug into the bloodstream. (a) show lim t-->infinity...

y= sin^2 [cos√(sinπx)] what is the derivative chain rule?