### Home > APCALC > Chapter 3 > Lesson 3.1.2 > Problem3-28

3-28.

Write slope functions for the following functions:

1. $f(x) = 7x^2$

Use the Power Rule. If $f(x)=ax^n$, then $f^\prime (x) = nax^{n−1}$.

$f^\prime (x) = 14x$

1. $f(x)=\pi^2$ (Careful!)

Remember that $\pi$ is just a number, not a variable!

Since $\pi\approx3$, what is the slope function of $y=3^2$? Use that to find the slope function of $f(x)=\pi^2$.

1. $f(x) = 2(x – 2)^4 + 18x$

$f(x)$ is a horizontal shift of $y = 2^4+18x$, whose slope function is easy to find with the Power Rule (see hint in part (a)). As for $f(x)$, THINK! Since slopes will shift with the function... $f^\prime (x)$ will equal a shifted version of $y^\prime$.

$f^\prime (x) = 8(x−2)^3+18$

1. $f(x) = \frac { 1 } { 3 }x^6 + 2x^4 − 3$

See hint in part (a).