Question

Please help!

Answer 1

The derivative of $f(x) = 2\cdot x^{2}-9$ is $f'(x) = 4\cdot x$.

In this exercise we must apply the definition of derivative, which is described below:

$f'(x) = \lim_{x \to 0} a_n \frac{f(x+h)-f(x)}{h}$ (1)

If we know that $f(x) = 2\cdot x^{2}-9$, then the derivative of the expression is:

$f'(x) = \lim_{h \to 0} \frac{2\cdot (x+h)^{2}-9-2\cdot x^{2}+9}{h}$

$f'(x) = 2\cdot \lim_{h \to 0} \frac{x^{2}+2\cdot h\cdot x + h^{2}-2\cdot x^{2}}{h}$

$f'(x) = 2\cdot \lim_{h \to 0} 2\cdot x + h$

$f'(x) = 4\cdot x$

The derivative of $f(x) = 2\cdot x^{2}-9$ is $f'(x) = 4\cdot x$.

We kindly invite to check this question on derivatives: brainly.com/question/23847661