Let f and g be the functions in the table below. x

Let f and g be the functions in the table below. x | f(x) | g(x) | f '(x) | g'(x) --|------|------|--------|------- 1 | 3 | 2 | 4 | 6 2 | 1 | 3 | 5 | 7 3 | 2 | 1 | 7 | 9 (a) If F(x) = f(f(x)), find F '(3). F '(3) = (b) If G(x) = g(g(x)), find G'(1). G'(1) =

Transcript

00:01 In this question, we are given the values of f, g, f prime and g prime at different values at x equals 1, 2 and 3.

00:09 And i apologize, i forgot to fill out the column for g prime, so it's going to be 6, 7 and 9.

00:17 Oh, sorry, i did that.

00:21 I did that the column 6, 7 and 9 is supposed to be the column for g prime.

00:28 And a column for f prime is 4, 5, 7.

00:37 And we're asked to find f capital prime of 3, where f capital of x is f of f of x.

00:46 So first let's find the general formula for f capital prime of x.

00:50 And to do that we need to use the chain rule.

00:53 But note that the function consists of two parts, the outer part and the inner part.

01:00 So by the chain rule, we need first to differentiate the outer part and then multiply this by the derivative of the inner part.

01:12 Now we can calculate f prime of 3.

01:15 F prime of 3 equals to f small prime of f of 3 times a small prime of 3.

01:25 Now we need to look up the values in the table.

01:29 We need a small prime of 3.

01:32 So we need to find the column for f prime, f small prime and the column and the row for 3.

01:39 And at the intersection we are going to get 7.

01:42 So a small prime of 3 equals to 7.

01:46 We also need to look up the value of f of 3.

01:49 So we need to find the column for f and the row for 3 and the entry at the intersection is 2.

01:59 So we are going to get that f capital prime of 3 equals to f prime or f small prime of 2 times 7.

02:08 Now we need to look up a small prime of 2 in the table...

Question

Let f and g be the functions in the table below. x | f(x) | g(x) | f '(x) | g'(x) --|------|------|--------|------- 1 | 3 | 2 | 4 | 6 2 | 1 | 3 | 5 | 7 3 | 2 | 1 | 7 | 9 (a) If F(x) = f(f(x)), find F '(3). F '(3) = (b) If G(x) = g(g(x)), find G'(1). G'(1) =

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