For the function f(x) = ax^2 - 2bx + 5

Question

a) Compute f'(x)

b) Compute a and b such that the slope of the tangent line at x = 0 is 2 and f'(1) = 4

Answer 1

f(x) = ax² - 2bx + 5

f'(x) = 2ax - 2b

Slope of tangent line at x = 0 is f'(0) = -2b = 2. So, b = -1

f'(x) = 2ax -2(-1) = 2ax + 2

f'(1) = 2a + 2 = 4

So, a = 1.

Answer: a = 1 and b = -1