# How do you use the second derivative to determine concave up / down for #f(x) = 3x^3-18x^2+6x-29#?

##### 2 Answers

Refer Explanation Section

#### Explanation:

At the out set, it is a cubic function. It has two turning points.

When the function is minimum, the curve is concave upwards.

When the function is maximum the curve is concave downwards.

Find the first derivative.

Set it equal to zero.

It is a quadratic equation. It has two x values.

Find the second derivative.

Substitute the already calculated values of x to decide whether the function has a minimum or maximum.

At x = 3.82 The second derivative is positive. The function has a minimum. At this point the curve is concave upwards.

At x = 0.17. The second derivative is negative. The function has a maximum. At this point the curve is concave downwards.

The graph of

#### Explanation:

The graph of

Because this

This cuts the number line into two pieces:

on

on

So the graph of

Because