We want to stop moving along the line as soon as we come to the first maximum. T

Question

We want to stop moving along the line as soon as we come to the first maximum. Take the derivative of f(l(t)) with respect to t, set it equal to 0 and find where the maximum occurs. The maximum you found is t0, the first stopping time. If we follow l(t) for longer than to, we begin to descend, so we stop exactly at t0. Find (x1, y1) by plugging t0 into l(t). Repeat this entire process starting at (x1, y1). If done correctly, the next point you stop at should be the maximum. Remember, you can use any vector parallel to the gradient as the direction for your line, so pick one that is nice to plug into f(x, y). To check your answer, plug your second stopping point into the gradient. If the gradient is zero at this point, you have found the maximum of f(x, y). Congratulations!

Explanation / Answer

4) for maxima

derivative of f(l(t) = 0

d/dt(f(l(t)) = 0

f`(l(t)) * l`(t) = 0

5) x1 = l(t0)

y1 = f(l(t0))

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