Calculus Help math

Question

Find the values of a and b so that the parabola y = ax2 + bx has a tangent line at (1, −9) with equation y = −x − 8.

Let h(x) = 7g(x) 8 + f (x) . Suppose that f (2) = −1, f '(2) = 3, g(2) = −2, and g'(2) = 3. Find h'(2).

Answer 1

Substitute (1,-9) into the equation to get -9 = a + b.

The derivative at (1,-9) must be -1 = 2a + b

Solving these simultaneously gives a=8 and b=-17

For the second part, all you need to know is h'(x)=(7/8)g'(x) + f'(x), then plug in x=2