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

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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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um, this is one off the graph. A sketch for this problem. Um, first, we noticed that this f on the function f is an old function. Let me in this work we only folk song zero to infinitely and no enough. The other part of the Red Line parties that were this symmetry about X equals zero. Okay, So from the information we know from 0 to 2, um, from X from 0 to 2, um, f is increasing and the front foot infinity if it's decreasing and we already know, uh, X equal to three, there's an inflection points. This is the inflection point on its right. The curve is coming down and on council left the cave The coffee's can kept on and on to Writer Kofi's concrete. Also, there's the horizontal seem totally xy costa. What here since like this, Why coast once or so westway finish the positive parts. We just do the symmetric Ah, curve for the negative part and that's there. So be careful about this. If we don't asymmetry curve, another sympathetic um horizontal syntactic will be X equals two minds. Why? It cost to minus one

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