CPM Homework Help : CALC Problem 3-73

Given f(x) below, find f ′(x). Homework Help ✎
1. f(x) = −x³
4. f(x) = 3 sin(x + π)

Hint (a):

Use the Power Rule.

Hint (b):

f(x) can be rewritten with a negative exponent.

Hint (c):

f(x) can be rewritten with a fractional exponent.

Hint (d):

You know that the derivative of y = sinx is y' = cosx. Well, f(x) is a transformation of y = sinx. So f '(x) (its slope function) will be a transformation of cosx.

Hint (d):

The 3 represents a vertical stretch. How will that transform the derivative (slope) of y = sinx? The +π represents a horizontal shift. How will that transform the derivative (slope) of y = sinx?

Answer (d):

The derivative will also be shifted π units to the left and stretched by a factor of 3.