Question

Functions f , g. and h are twice-differentiable functions with g(5)=h(5)=1. The line y=1- 5/3 (x-5) is tangent to both the graph of g at x=5 and the graph of h at x=5

(a) Find g'(5)

Answer 1

To find g'(5), we need to use the given information that the line y = 1 - 5/3 (x - 5) is tangent to the graph of g at x=5. Since the line is tangent, it means the derivative of g(x) at x=5 is equal to the slope of the line. First, we find the slope of the line by identifying the coefficient of x (which is -5/3). Therefore, g'(5) = -5/3.

Step-by-step explanation:

To find g'(5), we need to use the given information that the line y = 1 - 5/3 (x - 5) is tangent to the graph of g at x=5.

Since the line is tangent, it means the derivative of g(x) at x=5 is equal to the slope of the line.

First, we find the slope of the line by identifying the coefficient of x (which is -5/3). Therefore, g'(5) = -5/3.