Question

complete the sentence below.
the function ( f(x)=x^{2} ) is decreasing on the interval

the function ( f(x)=x^{2} ) is decreasing on the interval

Explanation:

Step1: Find the derivative of the function

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

Step2: Determine where the derivative is negative

A function \(y = f(x)\) is decreasing when \(f^\prime(x)<0\). Set \(f^\prime(x)=2x<0\). Solving the inequality \(2x<0\) (divide both sides by 2, the inequality sign remains the same since \(2>0\)), we get \(x < 0\).

Answer:

\((-\infty,0)\)