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

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

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

Answer

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))