### Home > CALC > Chapter 3 > Lesson 3.1.2 > Problem 3-28

3-28.

Find slope functions,

*f*′(*x*), for the following functions: Homework Help ✎*f*(*x*) = 7*x*^{2}*f*(*x*) =*π*^{2}(Careful!)*f*(*x*) = 2(*x*− 2)^{4}+ 18*x*

Use the Power Rule.If *f*(*x*)=*ax ^{n}*, then

*f*'(

*x*) =

*nax*

^{n}^{−1}

*f* '(*x*) = 14*x*

Remember that π is just a number, not a variable!

Since *π* ≈ 3, what is the slope function of *y* = 3^{2}? Use that to find the slope function of *f*(*x*) = *π*^{2}.

*f*(*x*) is a horizontal shift of *y* = 2^{4}+18*x*, 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* '.

*f* '(*x*) = 8(*x*−2)^{3}+18

See hint in part (a).