Question

Given F(h)=9h+8 , find : f(3)

Answer 1

Answer: f(x) = x9h(x)

h(-1) = 2

h'(-1) = 5

We need to find h(x) first. Once we have h(x), we can find the derivative of f(x). Then evaluate the derivate when x = -1.

We know that derivative is the slope of the tangent line. In this case, the slope of the line tangent to h(x) at x=-1 is 5.

h(-1) = 2 has a coordinate point of (-1, 2).

2 = 5(-1) + b

2 = -5 + b

7 = b

h(x) = 5x + 7 -----> equation of the tangent line

f(x) = x9(5x + 7)

f(x) = 5x10 + 7x9

Take the derivative of f(x).

f'(x) = 50x9 + 63x8

f'(-1) = 50(-1)9 + 63(-1)8

f'(-1) = -50 + 63

f'(-1) = 13

Explanation:

Answer 2

f(3) = 35

Explanation:

Since we are given f(3), that means h = 3

f(3) = 9(3) + 8

f(3) = 27 + 8

f(3) = 35

Best of Luck!