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15 October, 06:31

Use the table below to evaluate the derivative with respect to x of g of f of 2 times x at x = 1.

__x | 1 | 2 | 3 | 4

f (x) 6 1 8 2

f' (x) 6 1 8 2

g (x) 1 4 4 3

g' (x) 9 5 5 - 4

+3
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  1. 15 October, 07:29
    0
    (g o f) (2x) = g (f (2x))

    take derivitive

    use chain rule

    remember

    derivitive of g (f (x)) = g' (f (x)) f' (x)

    so

    g (f (2x)) = g' (f (2x)) f' (2x) (2)

    at x=1

    f (2x) = f (2) = 1

    g' (1) = 1

    f' (2x) = f' (2) = 1

    we get

    (1) (1) (2) = 2

    it is 2

    I hope yo udidn't copy the wrong value for f (x) or f' (x)
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