Is $f (x) = 10 x^{5} - 7 x^{4} + x - 4$ $f(x)=10x^5-7x^4+x-4$ concave or convex at $x = - 1$ $x=-1$ ?

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Answer 1 · 2017-07-20T06:03:08

f is concave at $x = - 1$ $x=-1$

We will find the second derivative and substitute the given value of x; if $f''(-1)>0$ then it is convex:

$f'(x)=50x^4-28x^3+1$

$f''(x)=200x^3-84x^2$

$f''(-1)=-200-84<0$

Then f is concave at $x=-1$
graph{10x^5-7x^4+x-4 [-5, 2, -40, 2]}

Is f(x)=10x^5-7x^4+x-4f(x)=10x5−7x4+x−4f(x)=10x^5-7x^4+x-4 concave or convex at x=-1x=−1x=-1?