Find the intervals of concavity from the derivative graph

The video tutorial explains how to find intervals where a function is concave up by analyzing the first and second derivatives. It emphasizes the importance of the second derivative being positive and relates this to the slope of the first derivative. The tutorial identifies specific intervals where the second derivative is positive, indicating concavity.

What is the primary focus when determining where a function is concave up?

• The second derivative

• The integral of the function

• The first derivative

• The value of the function itself

For a function to be concave up, what must be true about its second derivative?

• It must be positive

• It must be zero

• It must be negative

• It must be undefined

How is the second derivative related to the slope of the first derivative?

• It is unrelated to the first derivative

• It is the slope of the first derivative

• It is the inverse of the first derivative

• It is the integral of the first derivative

Which interval is identified as having a positive slope for the first derivative?

• From -3 to 2

• From 2 to 5

• From 0 to 3

• From 7 to 10

Why is the interval from 5 to 7 significant in terms of concavity?

• The second derivative is negative

• The slope of the first derivative is positive

• The first derivative is zero

• The function is decreasing