Question

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

Answer 1

Remember the quotient rule

$\frac{dy}{dx} \frac{f(x)}{g(x)}= \frac{f'(x)g(x)-g'(x)f(x)}{g(x)^2}$

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
$\frac{dy}{dx} \frac{top}{bottom}= \frac{top'bottom-bottom'top}{bottom^2}= \frac{(6x-8)(7x^2+6x+9)-(14x+6)(3x^2-8x+4)}{(7x^2+6x+9)^2}$
if we simplify it we get
$\frac{2(37x^2-x-48)}{(7x^2+6x+9)^2}$
subsituting x=4
$\frac{216}{4205}$