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**Open that Hampster!** 1) $\displaystyle S(t) = 160t-16t^2$

A- Derive the equation (simple) and find the critical numbers. The derivative of position is velocity, so if you think about it when you throw a ball in the air, the top of the arc is a point where the ball has no velocity (just after it stops going up but before it starts falling), so it's simple. After you have the derivative find where it's equal to 0 (critical numbers), and the largest S for those t is your answer.

B- Set S(t) = 0 and solve. 0 isn't the answer.

3) Find the derivative of [tex]F(x) = e^{sin2x}

Use the Chain Rule. $\displaystyle u(x) = e^x$; $\displaystyle v(x) = sin2x$. You'll have to use the Chain Rule again on v(x) to find the derivative.

8) Where are you stuck? You should be able to write the function as $\displaystyle F(x) = 2((sinx)(sinx)) + 2((cosx)(cosx))$ and just solve as the product rule.