Question

`f` is some differentiable function. `f'`, the derivative of `f` is shown below [note, is not the graph of f itself]. Use the graph to answer the following questions [For parts (a)-(c), select all that apply]? (See image below)

Answer 1

See below.

Explanation:

`f` is increasing where `f'` is positive. That is, where the graph of `f'` is above the `x` axis.

`f` is decreasing where `f'` is negative. That is, where the graph of `f'` is below the `x` axis.

The critical values are the `x` intercepts.

Without knowing the function, we cannot find the minima and maxima (or minimums and maximums, if you insist).

But we CAN find the `x` values where minima occur.

`f` has a minimum where `f'` changes from negative to positive. (In this example at `x=-4` and at `x=1`.)

`f` has a maximum where `f'` changes from positive to negative. (In this example at `x=3`.)