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Suppose $f^{\prime \prime}$ is continuous on $(-\infty, \infty)$(a) If $f^{\prime}(2)=0$ and $f^{\prime \prime}(2)=-5,$ what can you say about $f ?$(b) If $f^{\prime}(6)=0$ and $f^{\prime \prime}(6)=0,$ what can you say about $f ?$

A. $f(2)$ is a critical point, and is a local maximum.B. horizontal tangent at $x=6$

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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I'm in this question when to describe, um, some fact off the function by phone that given information. So for party, we know that, um, if has a horizontal attention line at X equals 22 amuse xy question to it's a critical point. Did you see it was a critical point. Also, by the secularity of test Since the second of purity of at X equals tourist inactive them. Use X equals there to is no co mix. So we can have this information from part eight and for Poppy. Well, we only know that there is a horizontal tend your line. Um, at X equals six. We don't know if this is a local maximum. Hello, committeeman. Or neither. Because the second of the narrative at this point is zero. So the second figurative test is inconclusive. So this is the only factory no.

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