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Asked Dec 16, 2019
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23. If f(5) = 4, fi(5) = –1, g(5) = 2, and g/(5) = -3, find h/(5) for each of
the following functions:
f(x)
iv) h(x) = (f(x))².
g(x)
i) h(x) = 2f(x)–3g(x) ii) h(x) = f(x)g(x) (iii) h(x) =
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23. If f(5) = 4, fi(5) = –1, g(5) = 2, and g/(5) = -3, find h/(5) for each of the following functions: f(x) iv) h(x) = (f(x))². g(x) i) h(x) = 2f(x)–3g(x) ii) h(x) = f(x)g(x) (iii) h(x) =

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Expert Answer

Step 1

Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.

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Given: S(5) =4, f"(5)=-1,g(5)=2, g'(5)=-3 Find: h'(5).

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Step 2

Part (i):

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h(x)=2f(x)-3g (x) Differentiate h with respect to x. Apply constant multiple rule. h'(x)=2f'(x)-3g'(x) Substitute x =5. h'(5)=2f"(5)-3g'(5) =2x(-1)-3×(-3) =-2+9 =7

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Step 3

Part (ii):

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h(x)=f (x)g(x) Differentiate h with respect to x, Apply Product rule. h'(x)= f (x)g'(x)+g(x)f'(x) Substitute x =5. h'(5) = f (5)g'(5)+g(5)S"(5) =4x(-3)+2×(-1) =-12-2 =-14

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Math

Calculus