Question

Please help asap. Really would appreciate it

Answer 1

Explanation:

We got

`(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

`(0)/(0)`

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

`(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.