Problem 16 Medium Difficulty

Sketch the graph of a function $g$ for which
$$\begin{array}{l}{g(0)=g(2)=g(4)=0, g^{\prime}(1)=g^{\prime}(3)=0} \\ {g^{\prime}(0)=g^{\prime}(4)=1, g^{\prime}(2)=-1, \lim _{x \rightarrow \infty} g(x)=\infty, \text { and }} \\ {\lim _{x \rightarrow-\infty} g(x)=-\infty}\end{array}$$

Answer

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Video Transcript

so we want to do is good. Graph the function G This Jesus. Uh did you have to Ziegel to cheer for And she's all equal to zero e prime of one is equal to G crime three, which is equal to zero seeing g prying zero is able to g prime for it was a good one d go just check his honesty. G prime of 32 Well, Jake's a negative one. Andi limit as X goes to infinity nog necks, It's positive. Infinity. I'm Lim as X goes to negative infinity of G vex is negative. So how come with you? Well, we're gonna start as usual the graph. You know that zero two and four G passes through 0 to 4. Furthermore, we know that slope that one is flat on a slope. Three is flat and we know that slope. That one. I'm sorry. Zero It's positive in the slough at four. It's positive slow but two is negative One. So bearing this in mind, you know that's slope at 10 on the slope it 3 to 0. We also know that the limit as X approaches infinity is infinite. When the slope is its approach is negative. Infinity is negative. Hope that helps