Georgia Southern University

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Problem 66

Sketch the graph of a differentiable function $y=f(x)$ that has

a. a local minimum at $(1,1)$ and a local maximum at $(3,3)$

b. a local maximum at $(1,1)$ and a local minimum at $(3,3)$

c. 1 ocal maxima at $(1,1)$ and $(3,3)$

d. local minima at $(1,1)$ and $(3,3)$ .

Answer

See graphs.

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## Discussion

## Video Transcript

Okay, So you want to sketch the graph of the different triple function and Okay, so it's stroller graph. Thanks. Bye. It looks like it's just a TV screen, and okay, that has a local minimum in a local maximum. So we're gonna We're gonna need multiple colors. Will have a seeing hand t. Okay, so for a wee want a local minimum at one one in a local maximum at thirty three. OK, so, technician, just something like that. Okay, So have a local minimum at one one. Welcome, Max. One of the thirty three. Then we could be We want a local maximum and one one in a local minimum at three. Three. So we gotta have a local maximum one one, a local Maxima, and then we want to have a local minima at three. Three. So we better go above three. Three. I think it's down. Yeah. Okay, good. So you see, we have a local max one one and a local minimum. Three three. You never see. We want local Maxima at one one and three three. Okay, so we'll do something like so you know, look, Max on one and then a local Max three, three. Okay. And then finally function with a local minima one one in a local minima three three No. Okay, there you go. And hopefully those functions, like different doble they're supposed to be.

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