Question

Use the figure below to estimate the indicated derivatives, or state that they do not exist. If a derivative does not exist, enter dne in the answer blank. The graph of f(x) is black and has a sharp corner at x=2. The graph of g(x) is blue.

Answer 1

Well, try using the product rule on this:

h(x)=f(x)g(x)

to find h'(x)

Answer 2

I am not sure how to do that from the given graph

Answer 3

Don't worry about the graph, just use the product rule on the algebra, I know it's kind of strange so I'll show you:

h(x)=f(x)g(x)

now to differentiate we just do the same thing to both sides:

h'(x) = [f(x)g(x)]'

Now we can evaluate this a little further by using the product rule:

[f(x)g(x)]'=f'(x)g(x)+f(x)g'(x)

So now you have a full equation for h'(x) in terms of stuff you can find!

h'(x) = f'(x)g(x)+f(x)g'(x)

Answer 4

okay, i know that, but what do i use as my F(x) and g(x)?

Answer 5

You obtain those directly off of the graph there, so for instance f(1)=1.5 and you can tell because f is a straight line with a -1/2 slope if you look at it it directly hits integer points on either side.

Answer 6

okay well the only one i am having trouble with is h'(3)