Question

Is `f(x) = 8x^4+3x^3 + 4x^2+x-lnx` concave or convex at `x=11`?

Answer 1

Concave

Explanation:

Find the second derivative.

`f'(x) = 32x^3 + 9x^2 + 8x + 1 - 1/x`

`f''(x) = 96x^2 + 18x + 8 + 1/x^2`

This is positive at `x = 11`, so therefore concave.

Hopefully this helps!