CPM Homework Help : CALC Problem 3-15

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3-15.

Remember the conjecture developed in problem 3-5 and find the slope function, $f'(x)$ , for each of the following functions.

$f(x) = x^9$
Hint 1(a):
BASIC CONJECTURE that you should have made during class: The slope function is one-degree lower than the original function.
Hint 2(a):
ADVANCED CONJECTURE that you might have made during class:The slope function is one degree lower than the original function AND stretched by the degree of the original function.
Answer (a):
slope function $= 9x^8$

$f(x) = x^{13}$
Hint (b):
Refer to hint for part (a).

$f(x) = 2x$
Hint (c):
This one does not require a conjecture - an Algebra I student could do it! This is the equation of a straight line. What is its slope?

$f(x) = 6$
Hint (d):
Refer to hint for part (c).

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