Find the absolute extrema of f(x) = e^{x^2+2x}f ( x ) = e x 2 + 2 x on the interval [-2,2][ − 2 , 2 ] first and then use the comparison property to find the lower and upper bounds for i = \displaystyle \int_{-2}^{2} f(x) \, dxi = ∫ − 2 2 f ( x ) d x.

has critical points where the derivative is 0:

The second derivative is

and , which indicates a local minimum at with a value of .

At the endpoints of [-2, 2], we have and , so that has an absolute minimum of and an absolute maximum of on [-2, 2].

So we have

the distance from any point on the parabola to the focus is the exact same as the distance from that point to the directrix.

if you could provide answer choices that might allow me to answer the question easier if my above answer isn't an option! (: