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Sketch the graph of a function that satisfies all of the given conditions.$f^{\prime}(0)=f^{\prime}(2)=f^{\prime}(4)=0,$$f^{\prime}(x)>0$ if $x < 0$ or $2 < x < 4,$$f^{\prime}(x) < 0$ if $0 < x < 2$ or $x>4,$$f^{\prime \prime}(x)>0$ if $1 < x <3, \quad f^{\prime \prime}(x) <0$ if $x<1$ or $x>3$

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Calculus 1 / AB

Chapter 4

APPLICATIONS OF DIFFERENTIATION

Section 3

Derivatives and the Shapes of Graphs

Derivatives

Differentiation

Applications of the Derivative

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University of Michigan - Ann Arbor

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one off the example satisfy the condition in this question. Looks like this on. So first we realize that we have, um, three quick points at X equals zero to in the four. So off these three points have horizontal tend your lines. And the second we notice that, um when exist, lesson zero it's increasing when X is from the 02 to should be decreasing when x thrown. Tutu's four you see increasing again and when exceeds greater Foresti crazy. So, um, we have this, um, increasing and decreasing property here and therefore the can cavity when x it's less long. One. It's Kong cave. Um, it's conquered down like this and at Exit Coast one, there's an inflection point. So the continuities are different on the two side. Off X equals to one. And there for the same reason. When X equals three, there's another inflection point, their communities that different. This is, um, one of the example satisfied all the conditions in that in this question,

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