Posted by Subhotosh Khan on October 16, 2002 at 09:24:20:
In Reply to: Re: Calculus f' and f'' posted by Joel on October 16, 2002 at 00:44:29:
: : 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
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