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)=(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{ }(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.