Question

The function f(x)=7x^3+4x has an inverse function g .Find g'(0) and g'(11)

Answer 1

first, we have to find g(x)

g(x)=1/f(x)

=1/(7x^3 + 4x)

this simplifies to be

1/4x - 7x/(4(7x^2 + 4))

so, we can find the d d x of g(x)

this turns that

g'(x) =

.

evaluating with x=0 and x=11,

we get g'(0) tends to infinity

while g'(11)=

$- \frac{2545}{87628321}$

hope this helps you...