Question

Use the given graph of f(x) to sketch the graph of f’(x).

Answer 1

would this be it, its derivative?

Answer 2

Your original graph has 3 "humps" in it, indicating that it is a quartic function, that is, a polynomial of degree "4", meaning that the derivative function will be a cubic, or a polynomial of degree "3". Confirming that is the fact that the derivative as "x" goes to negative infinity will be negative and the derivative as "x" goes to positive infinity will be positive. The derivative function will then have 2 "humps". This is for starters. The general shape of your graph suggests that you know this either well or sort of in an intuitve way.

Answer 3

okay

Answer 4

ok, but we're not done. Hold on, I have more typing.

Answer 5

ok

Answer 6

okay got you

Answer 7

okay

Answer 8

The only problem with your graph is that you have it crossing the x-axis 3 times. That would not be the case because we can start by looking at that minimum. There we have the derivative as "0" and only at that point. As you go from that "x" "to the left", you will see that the derivative is always negative, even at the point (0, 0), so you will never get back to 0. Therefore, the graph will look more like: