g. determine the value of x that f(x) = 2x^2 - 8 increasing.

Explanation:

Step1: Find the derivative

The derivative of $f(x)=2x^{2}-8$ using the power - rule $(x^n)' = nx^{n - 1}$ is $f'(x)=4x$.

Step2: Set up the inequality

A function is increasing when $f'(x)>0$. So we set up the inequality $4x>0$.

Step3: Solve the inequality

Dividing both sides of $4x>0$ by 4 gives $x > 0$.

Answer:

$x>0$