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If f and g are differentiable functions for all real values of x such that f(2) = 5, g(2) = 3, f '(2) = 1, g '(2) = -2, then find h '(2) if h(x) = f(x) g(x).

Respuesta :

xKelvin

Answer:

[tex]h'(2)=-7[/tex]

Step-by-step explanation:

So we have:

[tex]h(x)=f(x)g(x)[/tex]

Differentiate. Use the product rule:

[tex]h'(x)=f'(x)g(x)+f(x)g'(x)[/tex]

Substitute 2 for x:

[tex]h'(2)=f'(2)g(2)+f(2)g'(2)[/tex]

We know that f'(2) is 1, f(2) is 5, g(2) is 3, and g'(2) is -2. Make the appropriate substitutions:

[tex]h'(2)=(1)(3)+(5)(-2)[/tex]

Simplify:

[tex]h'(2)=3-10[/tex]

Subtract:

[tex]h'(2)=-7[/tex]

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