Question

Two students in your class, Isaac and Noah, are disputing a function. Isaac says that for the function, between x = −1 and x = 1, the average rate of change is 0. Noah says that for the function, between x = −1 and x = 1, the graph goes up through a turning point, and then back down. EXPLAIN how Isaac and Noah can both be correct, using complete sentences.

Answer 1

Both of them are correct.

Explanation:

Isaac says that for the function, between x = -1 to x = 1, the average rate of changes is 0.

When a function has the average rate of change = 0 i.e.
`(dy)/(dx)=0`,

We get that the function will have an extrema point i.e. a point at which the function will have the largest or smallest value i.e. the graph of the function changes its direction.

Further, Noah states that between x = -1 to x = 1, the graph goes up through a turning point and then goes back down.

This means that in x = -1 to x = 1, the function attains the maximum value at some point through which graph is changing its direction from upwards to downwards.

As, both Isaac and Noah are stating that there is a point in x = -1 to x = 1, at which the function attains its maximum value and the graph changes its direction.

Hence, both of them are correct.