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Alex
3 years ago
13

100 POINTS, WILL MARK BRAINLIEST! If h(x) = f[f(x)] use the table of values for f and f ′ to find the value of h ′(1).

Mathematics
2 answers:
cricket20 [7]3 years ago
6 0

Answer:

h'(1) = 5

Step-by-step explanation:

So, we know that h(x) = f[f(x)].

We can use what we are given for f(x) and f'(x) to solve.

If we use x = 1,  we can substitute.

h(1) = f[f(1)]

Looking at the table, we know that f(3) = 6, f(2) = 1, and f(1) = 3.

Now solve for h'(1). Note that x = 1.

h'(1) = f[f(1)]

Using the table we know that f'(1) = 2 and f'(2) = 5.

So, h'(1) = 5

Best of Luck!

victus00 [196]3 years ago
4 0

Answer:

The value of h^\prime(1)=5

Step-by-step explanation:

Given that  h(x)=f(f(x))

now to find h(x)=f(f(x)) from the given functions f(x) and f'x

let h(x)=f(f(x))

Then put x=1 in above function we get

h(1)=f(f(1))

=f(3) (from the table f(1)=3 and f(3)=6)

Therefore h(1)=6

Now to find h'(1)

Let

h^{\prime}(x)=f^{\prime}(f^\prime(x)) (since  h(x)=f(f(x)) )

put x=1 in above function we get

h^{\prime}(1)=f^{\prime}(f^\prime(1))

=f^{\prime}(2)    (From the table f^\prime(1)=2 and f^\prime(2)=5)

h^{\prime}(1)=5

Therefore h^{\prime}(1)=5

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