# math

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f(x)=x^4-4x^3+10

Where are the relative extrema, if they exist?

• math -

x = 0 or x = 3

so
f(0) = 10
f(3) = 81 - 108 + 10 = -17

f '' (x) = 12x^2 - 24x

f '(0) = f ''(0) = 0
so (0,10) is a point of inflection

f ''(3) = 108 - 72 > 0
so at (3,-17) the curve is concave upwards, so
(3,-17) is a minimum point

look at the sketch

http://www.wolframalpha.com/input/?i=plot+x%5E4-4x%5E3%2B10

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