Question

Please help asap. Really would appreciate it

Answer 1

Step-by-step explanation:

We got

$\frac{f(x + h) - f(x)}{h}$

The function here is

9x^2 so we got now

$\frac{9(x + h) {}^{2} - 9 {x}^{2} }{h}$

$\frac{9( {x}^{2} + 2hx + {h}^{2} - 9 {x}^{2} }{h}$

$\frac{9 {x}^{2} + 18hx + 9 {h}^{2} - 9 {x}^{2} }{h}$

Cancel out terms.

$\frac{18hx + 9h {}^{2} }{h}$

If we direct subsitue we get

$\frac{0}{0}$

which is intermidate form in calculus so now, let try to find another way to evaluate this, we can factor out 9h

$\frac{9h(2x + h}{h}$

Cancel out h

$9(2x + h)$

Subsitue 0 for h.

$9(2x + 0)$

$9(2x)$

$18x$

The answer here is 18x.

Congrats. We just found the derivative of a function.