Question

For what values of x is `f(x)=x^4-x^3+7x^2-2` concave or convex?

Answer 1

Concave for all real numbers

Explanation:

Find `"f''(x)"`
When `"f''(x) ≥ 0"`, f(x) is Concave upward
When `"f''(x) ≤ 0"`, f(x) is Concave Downward

`f(x)=x^4−x^3+7x^2−2`
`f'(x) = 4x^3 - 3x^2 + 14x`
`"f''"(x)= 12x^2 - 6x + 14`

`"f''"(x) ≥ 0`
`12x^2 - 6x + 14 ≥ 0`
This is true for all real numbers => f(x) is concave upward for R.