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=(-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}`