Question

where is the function ( f(x)=x^{2} ) increasing? where is it decreasing?
the function ( f(x)=x^{2} ) is increasing on the interval
(type your answer in interval notation.)

Explanation:

Step1: Find the derivative of the function

The derivative of \(f(x)=x^{2}\) is \(f^\prime(x) = 2x\) (using the power rule \((x^n)^\prime=nx^{n - 1}\)).

Step2: Determine where the derivative is positive

Set \(f^\prime(x)>0\). So, \(2x>0\), which gives \(x > 0\).

Answer:

\((0,\infty)\)