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Evaluate f(x), evaluate f'(x) at x =4

Evaluate f(x), evaluate f'(x) at x =4-example-1

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remember the quotient rule


(dy)/(dx) (f(x))/(g(x))= (f'(x)g(x)-g'(x)f(x))/(g(x)^2)

k, so
top is 3x^2-8x+4, the deritivive of that is 6x-8
bottom is 7x^2+6x+9, deritivive is 14x+6

so

(dy)/(dx) (top)/(bottom)= (top'bottom-bottom'top)/(bottom^2)= ((6x-8)(7x^2+6x+9)-(14x+6)(3x^2-8x+4))/((7x^2+6x+9)^2)
if we simplify it we get

(2(37x^2-x-48))/((7x^2+6x+9)^2)
subsituting x=4

(216)/(4205)


User Theodore Tsirpanis
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