Review question

# What happens if we integrate, then differentiate? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8716

## Suggestion

For a positive number $a$, let $I(a) = \int_0^a \! \left(4 - 2^{x^2} \right) \, dx.$

Then $\dfrac{dI}{da}=0$ when $a$ equals

1. $\dfrac{1 + \sqrt{5}}{2}$,

2. $\sqrt{2}$,

3. $\dfrac{\sqrt{5} - 1}{2}$,

4. $1$.

We are looking for the stationary point of $I$. What does this mean geometrically?

As $a$ increases, for which points does $I(a)$ increase and for which points does it decrease? What does this tell us about where the stationary points have to lie?