dhiCup9caketter dhiCup9caketter

24-11-2016
Mathematics

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Sketch the graph of a function whose first derivative is always negative and second derivative is always positive.

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alsteva alsteva

27-11-2016

y = f(x)
y' < 0
y'' > 0

Function must be decreasing and concave

[tex]f(x)= e^{-x} \\ \\f'(x)=- e^{-x}\ \textless \ 0=-\frac{1}{e^x} \ \textless \ 0 \\ \\f''(x)=(-e^{-x})'=e^{-x}= \frac{1}{e^x} \ \textgreater \ 0[/tex]

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