hunterbrod336 hunterbrod336
  • 11-10-2019
  • Mathematics
contestada

If h(2)=7 and h'(2)=-2,find d/dx [(h(x))/(x)]
A. –11/4 B. 2 C. D. 8 E. 16

Respuesta :

steffaniasierrag
steffaniasierrag steffaniasierrag
  • 15-10-2019

Answer:

A. [tex]\frac{-11}{4}[/tex]

Remember that if f and g are functions with [tex]g(x)\neq 0[/tex] then, [tex]\frac{d}{dx}\frac{f(x)}{g(x)}=\frac{f'(x)g(x)-g'(x)f(x)}{g(x)^2}[/tex].

Then,

[tex]\frac{d}{dx}\frac{h(x)}{x}=\frac{h'(x)x-h(x)}{x^2}[/tex]

Evaluating in x=2,

[tex]\frac{h'(2)*2-h(2)}{2^2}=\frac{-4-7}{4}=\frac{-11}{4}[/tex]

Then the answer is A.

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