Question

look at the function f(x)=x3−5x 2+6 which describes an interval in which the function is increasing

Answer 1

Given data:

The expression for the given function is f(x)=x^3-5x^2+6.

The derivative of the given function is,

$\begin{gathered} f^{\prime}(x)=\frac{d}{dx}(x^3-5x^2+6) \\ =3x^2-10x \end{gathered}$

Equate the f'(x) to zero, and evaluate the values of x.

$\begin{gathered} 3x^2-10x=0 \\ x(3x-10)=0 \\ x=0,\text{ }\frac{10}{3} \end{gathered}$

Substitute -1 for x in the above expression.

$\begin{gathered} f^{\prime}(-1)=3(-1)^2-10(-1) \\ =3+10 \\ =13 \\ >0 \end{gathered}$

Positive sign indicate the given function is increasing in nature.