Originally Posted by

**sgcb** I need to find the maximum of this equation by finding the derivative and setting it to zero:

$\displaystyle f(x) = (1+20\sqrt{t})e^{-.05t} = e^{-.05t} + 20\sqrt{t}e^{-.05t}$

Now, solving for the derivative using the chain rule for the first operand, and using product rule+chain rule for the second operand, I get the following:

$\displaystyle f'(x) = \frac{10-t}{\sqrt{t}e^{.05t}} - \frac{.05}{e^{.05t}} = 0$

get common denominators:

$\displaystyle = \frac{10-t}{\sqrt{t}e^{.05t}} - \frac{.05\sqrt{t}}{\sqrt{t}e^{.05t}}$

Assuming that is correct so far, where do I go from there? Do I multiply through to cancel the denominator to get the following:

$\displaystyle 10 - t - .05\sqrt{t} = 0$

If that's correct, then what do I do?