Find the equation of the tangent line to yx at x 1 use y

Question

Use the values in the table below to answer each of the following:

a. Let p(x) = f(x) g(x)

Find p '(1) =

Does p(x) have a horizontal tangent at x = 1?

b. Let y (x) = f(g(x)).

Find the slope of y(x) at x = 1.

Find the equation of the tangent line to y(x) at x = 1. Use y for the dependent variable.

c. Let v(x) = (f(x))².

Find the value of v'' (1).

Is v(x) concave up or concave down at x = 1?

(d) Let r(x) = g(x) / x³

Find the exact value of r '(2).