Question

Consider the function f(x) = -2x^3 + 36x^2- 120x + 9.f(x) has an inflection point at x = Cwhere C is ___

Answer 1

Given:

$-2x^3+36x^2-120x+9$

Find- Inflection point.

Sol:

For inflection point

$\begin{gathered} f^{\prime}^{\prime}(c)=0 \\ \\ x=c \end{gathered}$

Derivative of function.

$\begin{gathered} f(x)=-2x^3+36x^2-120x+9 \\ \\ f^{\prime}(x)=-6x^2+72x-120 \\ \\ f^{\prime}^{\prime}(x)=-12x+72 \end{gathered}$

Check for zero then:

$\begin{gathered} f^{\prime}^{\prime}(x)=0 \\ \\ -12x+72=0 \\ \\ -12x=-72 \\ \\ x=\frac{-72}{-12} \\ \\ x=6 \end{gathered}$

The inflection point is x=c

so c is 6

$\begin{gathered} x=c \\ \\ x=6 \\ \\ c=6 \end{gathered}$