### Home > CALC > Chapter 4 > Lesson 4.1.2 > Problem4-20

4-20.

Differentiate each function below. That is, find its slope function, $f^\prime(x)$.

1. $f(x) = 6(x-2)^3$

You could expand $f(x)$ before you differentiate. Or...

You know that the derivative of $y = (x − 2)^³$ is $y^\prime= 3(x-2)^²$. What about the vertical stretch of $6$? If the $f(x)$ is stretched by a factor of $6$, what happens to its slopes/derivative? Are they stretched as well?

Strategy 1: $f^\prime(x) = 18x^²-72x + 72$
Strategy 2: $f^\prime(x) = 18(x-2)^²$

1. $f(x) = 2\operatorname{ sin }x$

What does the $2$ do to a sine graph? How will this affect the slope function?

1. $f(x) = (x + 5)(2x − 1)$

Before you differentiate, expand $f(x)$.

1. $f ( x ) = \frac { x ^ { 3 } - 6 x ^ { 2 } + 2 x } { x }$

Before you differentiate, simplify $f(x)$. But, don't forget that there was once a $0$ in the denominator... be sure to restrict the domain of the derivative.