Math Help Forum - View Single Post - f(x) graph based on derivative graph help

kalagota · #6 January 1st, 2009, 01:04 AM

Quote:

Originally Posted by Grandad

a) There are no maximum or minimum points in this interval

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c) As far as the sketch is concerned:

For $-3<x<-1$ , the gradient of the graph is positive, and it's increasing (because both $f'$ and $f''$ are positive), and tends to infinity as $x$ tends to $-1$ . So there's going to be an asymptote at $x=-1$ .
For $-1<x<1$ , gradient is negative but the graph is levelling out since $f''$ is positive and hence the gradient is increasing (i.e. becoming less negative)

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hmm, there is a possibility that at $x=-1$ , it is not asymptote. note that if $f(-1)$ exists, then the point $(-1,f(-1))$ is a pointed one (or is that a cusp?); thus if $f(-1)$ exists, then the point $(-1,f(-1))$ is a maximum point on this interval..

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