Is #f(x)=3/x-2x# concave or convex at #x=9/4#?

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Is #f(x)=3/x-2x# concave or convex at #x=9/4#?

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Answer 1 · 2016-02-14T00:47:31

Convex

Explanation:

Find the value of the second derivative at #x=9/4#. If the value is positive, then the function is convex. If it's negative, the function is concave at that point.

To find the function's second derivative, recall that #3/x=3x^-1# and then apply the power rule.

#f(x)=3x^-1-2x#

#f'(x)=-3x^-2-2#

#f''(x)=6x^-3=6/x^3#

The value of the second derivative at #x=9/4# is

#f''(9/4)=6/(9/4)^3#

This could be simplified, but it is evidently positive. Thus the function is convex at #x=9/4#.

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Is #f(x)=3/x-2x# concave or convex at #x=9/4#?

1 Answer

Explanation:

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