Question

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

Answer 1

f is concave at `x=-1`

Explanation:

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]}