### Home > PC > Chapter 9 > Lesson 9.3.4 > Problem9-143

9-143.

Let $h\left(x\right) = x^{2}$.

Find the general slope function at any $x$.

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

1. Compute $h ′\left(3\right)$.

Substitute the input value in the general slope function.

2. Compute $h ′\left(−2\right)$.

$−4$

3. Compute $h ′\left(a\right)$ for any fixed number $a$.

$2a$