# How do you find local min and max, point of inflection and concavity for the equation #f(x) = 4x^3 + 21x^2 - 294 +7#?

##### 1 Answer

The function has a minimum at

The function has a maximum at

At

#### Explanation:

Given -

Find the first derivative

Set it equal to zero. you are doing it to know for which value of 'x' the slope of the curve of the function becomes zero

Find the second derivative to judge for which value of "x" the function has a minimum, maximum and point of inflection.

At

At

Hence the function has a minimum at

At

At

Hence the function has a maximum at

To find the point of inflection, set the second derivative equal to zero

At