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Sketch a continuous graph that satisfies each set of conditions. d) f"(x)=1 when x>-2, f"(x)=-1 when...

Sketch a continuous graph that satisfies each set of conditions.

d) f"(x)=1 when x>-2, f"(x)=-1 when x<-2, f(-2)=-4

Math   Calculus   
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Homework Answers

Answer #1

Finding the equation of required curve

Similarly, for x < -2

And ,

For function to be continuous

where LHL is left hand limit, RHL is right hand limit.

Similarly,

The graph is continuous,

Graph:

before x<-2 concave down and then x>-2 concave up. Both the Graph and point x = -2 meet at y = -4.

this is rough sketch, graph can change depending on the value of constant we take. But concavity will remain same. As well as graph's monotonic behavior will look same.

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