Question

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

Answer 1

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)`