Question

Let f(x) = ∫ [-2, x^2 - 3x] e^t^2 dt
At what value of x is f(x) a minimum?

Answer 1

If f(x) = ∫[a,u] g(t) dt then df/dx = g(u) * du/dx
This is just the chain rule in reverse
df/dx = e^(x^2-3x)^2 (2x-3)
f(x) is a min or max when x = -3/2
So now, is it a min or a max? How can you tell?