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: