### Home > CALC > Chapter Ch3 > Lesson 3.1.1 > Problem 3-15

3-15.

Remember the conjecture developed in problem 3-5 and find the slope function,

*f*′(*x*), for each of the following functions. Homework Help ✎*f*(*x*) =*x*^{9}*f*(*x*) =*x*^{13}*f*(*x*) = 2*x**f*(*x*) = 6

BASIC CONJECTURE that you should have made during class:The slope function is one-degree lower than the original function.

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.

slope function = 9*x*^{8}

Refer to hint for part (a).

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?

Refer to hint for part (c).