CPM Homework Help : CALC Problem 3-28

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3-28.

Find slope functions, $f'(x)$ , for the following functions:

$f(x) = 7x^2$
Hint (a):
Use the Power Rule. If $f(x)=ax^n$ , then $f '(x) = nax^{n−1}$
Answer (a):
$f'(x) = 14x$

$f(x) = π^2$ (Careful!)
Hint 1(b):
Remember that π is just a number, not a variable!
Hint 2(b):
Since $\pi\approx3$ , what is the slope function of $y = 3^2$ ? Use that to find the slope function of $f(x) = π^2$ .

f(x) = 2(x − 2)⁴ + 18x
Hint (c):
$f(x)$ 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... $f'(x)$ will equal a shifted version of $y$ '.
Answer (c):
$f'(x) = 8(x−2)^3+18$

$f ( x ) = \frac { 1 } { 3 } x ^ { 6 } + 2 x ^ { 4 } - 3$
Hint (d):
See hint in part (a).

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