For what values of x is $f (x) = - 5 x^{3} + 2 x^{2} - 3 x - 12$ $f(x)= -5x^3+2x^2-3x-12$ concave or convex?

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Answer 1 · 2018-01-03T20:42:32

$f (x) = - 5 x^{3} + 2 x^{2} - 3 x - 12$ $f(x)=-5x^3+2x^2-3x-12$ , $D_f=RR$

$f'(x)=-15x^2+4x-3$

$f''(x)=-30x+4$

$f''(x)=0 <=> x=2/15$

For $x<2/15$ , $f''(x)>0$ so $f$ is convex at $(-oo,2/15]$
For $x>2/15$ , $f''(x)<0$ so $f$ is concave at $[2/15,+oo)$

For what values of x is f(x)= -5x^3+2x^2-3x-12 f(x)=−5x3+2x2−3x−12f(x)= -5x^3+2x^2-3x-12 concave or convex?