Lesson 61 — Maxima and Minima

Find the critical point of $$ and classify it using the second derivative test.

Classify the critical points of $$.

Find the absolute extrema of $$ on $$.

Classify all critical points of $$.

Find the absolute extrema of $$ on $$.

Find and classify the critical points of $$.

Analyze the critical points of $$.

Classify the critical point of $$.

Find the absolute extrema of $$ on $$.

Determine the absolute extrema of $$ on $$.

Determine the absolute extrema of $$ on $$.

Determine the absolute extrema of $$ on $$.

If $$ and $$, then the point $$ is:

Which statement about Fermat's Theorem is correct?

If $$ and $$, what is the correct conclusion?

Find the absolute extrema of $$ on $$.

Find the local extremum of $$.

Classify the local extrema of $$.

Find the absolute extrema of $$ on $$.

Find the extremum of $$ (Gaussian curve).

Find the absolute extrema of $$ on $$.

Determine the absolute extrema of $$ on $$.

A company sells a product with demand $$ units when the price is $$ reais. What price $$ maximizes total revenue?

A factory has cost $$ (reais) and revenue $$ producing $$ units. How many units maximize profit?

A model rocket is launched vertically, and its height (in meters) is $$. Determine the maximum height reached.

Find the local minimum of $$ for $$.

Determine the absolute extrema of $$ on $$.

Prove Fermat's Theorem: if $$ has a local maximum at $$ and is differentiable at $$, then $$.

Show that $$ has a critical point at $$, but this point is not a local extremum.

Show that $$ has a unique critical point and that this is the function's global minimum.