CPM Homework Help : PC Problem 9-143

Let h(x) = x². Homework Help ✎
1. Compute h ′(3).
2. Compute h ′(−2).
3. Compute h ′(a) for any fixed number a.

Hint:

Find the general slope function at any x.

Steps:

$\lim_{h\rightarrow 0}\frac{h(x+h)-h(x)}{x+h-x}=\lim_{h\rightarrow 0}\frac{(x+h)^{2}-x^{2}}{h}=\lim_{h\rightarrow 0}\frac{x^{2}+2xh+h^{2}-x^{2}}{h}=\lim_{h\rightarrow 0}\frac{2xh+h^{2}}{h}=\lim_{h\rightarrow 0}\frac{h(2x+h)}{h}=\lim_{h\to 0}2x+h=2x$

Hint (a):

Substitute the input value in the general slope function.

Answer (b):

−4

Answer (c):