# You are correct....Problem with semantics

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Posted by Subhotosh Khan on October 16, 2002 at 15:49:13:

In Reply to: ? Mr K ... posted by Joel on October 16, 2002 at 11:27:20:

: : : : I have a Calculus question here that I need help on.

: : : : Given a function, f(x), such that f'(a)=0 and f''(a)=8, what does this tell about y vs x?

: : : f'(a)=0 tells you that the slope of the graph of y=f(x) is 0 at the point x=a (in other words, a tangent to the curve at that point is horizontal). At this point, the curve exhibits one of the three critical points - maximum, minimum or saddle point - unless f' is zero everywhere.

: : : f"(a)= 8 (really, any positive number) tells you that the curve is concave upward at the point x=a. f"(a) =+ve means that the curve is exhibiting ***** a minimum or conacvr upward*****

: Isn't it true that if f''(a) is positive, the curve is DEFINITELY concave upward at this point and MAYBE there is also a minimum at this point?
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Yes - COMBINED with f'(a) = 0 -- f"(a)= +ve indicates minimum.

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