Question

If f is the function whose graph is shown below, let h(x) = f(f(x)) and g(x) = f(x2). Use the graph of f to estimate the value of each derivative.

find h'(2)
and g'(2)

i posted the graph in the comments

Answer 1

heres the picture idk if it works

Answer 2

hint:
we can write this:
\[\Large \begin{gathered}
h'\left( x \right) = f'\left( {f\left( x \right)} \right) \times f'\left( x \right) \hfill \\
\hfill \\
g'\left( x \right) = f'\left( {{x^2}} \right) \times \left( {2x} \right) \hfill \\
\end{gathered} \]

Answer 3

furthermore, from the graph, we get:
\(f(2)=1\), and \(f(2^2)=f(4)=2\)

Answer 4

i don't believe thats what i asked. i know how to derive h'(2) and g'(2) but i don't know how to find the values from the graph

Answer 5

the first derivative of f(x), is the slope of the tangent line to the graph at x=2

Answer 6

yes i understand that but i don't know how to find those values. everything i try is wrong

Answer 7

can you list the values for the slopes and i can take it from there.

Answer 8

as we can see, the slope of the tangent lines at x=1, and at x=2, are:
\(4/5\) and \(1\) respectively

Answer 9

they are approximate value of course

Answer 10

okay and what is the slope at x=4
(second part of the question)

Answer 11

I think it is \(4/2=2\) (approximated value)

Answer 12

hi, both answers were wrong for part a and b is there any way you can re-calculate (i have one more attempt to answer them on webbing)

Answer 13

I don't know, since it is difficult to establish the slopes of tangent lines from the picture
I suggest that you have to take a ruler, and then please draw the tangent lines you need, with the high accuracy, and measure the corresponding slopes

Answer 14

is there any way the slopes can be calculate another way besides finding the points