Question

Let h(x) = (1/4)x^3+2x-1 and let g be the inverse function of h. Notice that h(2)=5
g’(5)=?

Answer 1

Given that h(x) = (1/4)x^3+2x-1 and g is the inverse. By solving, will get g'(5) = 0.048

Step-by-step explanation:

To find the value of g'(5), we need to find the value of g'(x) and substitute x = 5 into the resulting function.

Since g is the inverse of h, we can find g'(x) using the formula:

g'(x) = 1 / h'(g(x))

First, let's find h'(x) by taking the derivative of h(x).

The derivative of (1/4)x^3+2x-1 is (3/4)x^2+2.

Now, we substitute x = g(x) into the derivative of h to find g'(x):

g'(x) = 1 / ((3/4)x^2+2)

Finally, substitute x = 5 into the equation to find g'(5):

g'(5) = 1 / ((3/4)(5^2)+2)

g'(5) = 0.048 (rounded to 3 decimal places).