# How to find the find local max, min and inflection points from an integral?

• Feb 17th 2010, 02:59 PM
skboss
How to find the find local max, min and inflection points from an integral?
I am trying to understand how to find the local max, min, inflection and critical points just by looking at the graphs from an Integral. Someone please help me.

The question says f(x)= x^2-5x-6 and F(x)= integral (0 to x) f(t) dt.

Find the critical points, local max, min and inflection points.

Solution:

Using the second FTC, I got

F(x) = integral (0 to x) (t^2-5t-6) dt

so F'(x) = x^2-5x-6
and the graph of this is included at the bottom. So from the graph I can understand that the critical points are -1 and 6 since F'(x) is the derivative of the integral.

But I don't know how to find local max,min and inflection points from this graph (given that it is the graph of the derivative of an antiderivative). Can anyone please help me find them/ explain them how to find it please?

(I know that to find local max, min and inflection points, I use the second derivative of a regular function. But I am not sure how to find them using the 2nd FTC)

• Feb 17th 2010, 03:58 PM
ione
Quote:

Originally Posted by skboss
I am trying to understand how to find the local max, min, inflection and critical points just by looking at the graphs from an Integral. Someone please help me.

The question says f(x)= x^2-5x-6 and F(x)= integral (0 to x) f(t) dt.

Find the critical points, local max, min and inflection points.

Solution:
Using the second FTC, I got

F(x) = integral (0 to x) (t^2-5t-6) dt

so F'(x) = x^2-5x-6
and the graph of this is included at the bottom. So from the graph I can understand that the critical points are -1 and 6 since F'(x) is the derivative of the integral.

But I don't know how to find local max,min and inflection points from this graph (given that it is the graph of the derivative of an antiderivative). Can anyone please help me find them/ explain them how to find it please?

(I know that to find local max, min and inflection points, I use the second derivative of a regular function. But I am not sure how to find them using the 2nd FTC)