For what values of x is $f (x) = - x^{3} + x^{2} - x + 5$ $f(x)=-x^3+x^2-x+5$ concave or convex?

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Answer 1 · 2017-10-22T23:46:20

Second derivative is positive and hence it is convex or minimum.

$f’(x) = -3x^2 + 2x -1$

$f”(x) = -6x + 2 = 0$
$6x = 2 or x = 1/3$

Therefore it is convex or minimum.

For what values of x is f(x)=-x^3+x^2-x+5f(x)=−x3+x2−x+5f(x)=-x^3+x^2-x+5 concave or convex?