For what values of x is $f (x) = - x^{4} - 9 x^{3} + 2 x + 4$ $f(x)= -x^4-9x^3+2x+4$ concave or convex?

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For what values of x is $f (x) = - x^{4} - 9 x^{3} + 2 x + 4$ $f(x)= -x^4-9x^3+2x+4$ concave or convex?

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Answer 1 · 2018-03-15T19:03:03

Convex for $x \in (- \frac{9}{2}, 0)$ $x in (-9/2 , 0)$

Concave for $x \in (- \infty, - \frac{9}{2}) \cup (0, \infty)$ $x in (-oo , -9/2 )uu(0,oo)$

Explanation:

A function is convex where its second derivative $f''>0$ , and concave where its second derivative $f''<0$

The second derivative is the derivative of the first derivative .i.e.

$f''=f'(f')$

$f'(x)=-4x^3-27x^2+2$

$f''(x)=f'(f'(x)=f'(-4x^3-27x^2+2)=-12x^2-54x$

Convex:

$-12x^2-54x>0$

$x(-12x-54)>0$

$x>0$

$-12x-54>0$

$-12x>54$

$x<-54/12$

$x<-9/2$

$x<0$

$-12x-54<0$

$x> 54/-12$ , $x> -9/2$

Convex for $x in (-9/2 , 0)$

Concave:

$-12x^2-54x<0$

$x(-12x-54)<0$

$x<0$

$-12x-54<0$ , $x> -9/2$

$x>0$

$-12x-54>0$ , $x<-9/2$

Concave for $x in (-oo , -9/2 )uu(0,oo)$

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For what values of x is $f (x) = - x^{4} - 9 x^{3} + 2 x + 4$ $f(x)= -x^4-9x^3+2x+4$ concave or convex?

1 Answer

Explanation:

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For what values of x is f(x)= -x^4-9x^3+2x+4 f(x)=−x4−9x3+2x+4f(x)= -x^4-9x^3+2x+4 concave or convex?

1 Answer

Explanation:

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For what values of x is $f (x) = - x^{4} - 9 x^{3} + 2 x + 4$ $f(x)= -x^4-9x^3+2x+4$ concave or convex?