# Maxima & Minima Question

#### OckLuke

##### New member
I’m struggling answering this question in my calculus studies. Can anyone help solve this?

#### Dr.Peterson

##### Elite Member
Sure. Just show us how far you have been able to get, and explain where and why you are stuck. Then we can give the appropriate help.

What did you get for the derivative? What did you do next?

#### OckLuke

##### New member
Thanks for the reply dr. Peterson.

I’m not 100% sure, but firstly would you just find the derivative of this using the general rule?

#### Dr.Peterson

##### Elite Member
Yes.

And when you aren't sure whether "the general rule" is appropriate, just try it and see how things work. You don't need to wait for permission. (That would have saved an hour ...)

To save some time, I'll ask the next question now: Are you allowed to use technology, such as a graphing calculator, to solve the resulting equation? It isn't going to be pretty.

#### OckLuke

##### New member
Okay. I’ll give that a go. I wouldn’t know where to head after that.
Yes, technology use is allowed

#### Otis

##### Senior Member
Okay. I’ll [find the first derivative of function h]. I wouldn’t know where to head after that … technology use is allowed
Local maximums and minimums always occur at values of t where the first derivative is zero (or undefined). So, the next step after you differentiate h(t) is to set that derivative equal to zero and solve for t. Use your technology to solve that equation.

h'(t) = 0

There are two Real solutions; one of them is the t-value at the local maximum, and the other is the t-value at the local minimum.

You can use the second-derivative test, to confirm which is which. Has your class covered how that test works?

#### Jomo

##### Elite Member
Local maximums and minimums always occur at values of t where the first derivative is zero (or undefined). So, the next step after you differentiate h(t) is to set that derivative equal to zero and solve for t. Use your technology to solve that equation.

h'(t) = 0

There are two Real solutions; one of them is the t-value at the local maximum, and the other is the t-value at the local minimum.

You can use the second-derivative test, to confirm which is which. Has your class covered how that test works?

Sorry but that is not 100% true on a closed interval, as we have in this problem. Local max and mins can occur at the endpoints and the derivative may not be 0 there..

#### Otis

##### Senior Member
… on a closed interval … max and mins can occur at the endpoints ….
Oh my. Yes, you're spot on, of course -- thank you for posting that. (A rookie mistake: peeking first at the graph of h versus thinking in general.)

#### Jomo

##### Elite Member
Oh my. Yes, you're spot on, of course -- thank you for posting that. (A rookie mistake: peeking first at the graph of h versus thinking in general.)

I did not hear you mention anything about corner time.

#### Otis

##### Senior Member
I did not hear you mention anything about corner time.
I don't know how to calculate the time.

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