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

##### 1 Answer

Oct 26, 2017

x = -1/2 with downward concavity

#### Explanation:

Concavity is expressed by the second derivative.

To start, we must take the first derivate to find the POINT(S):

What we just found are the extrema which we can simplify to mean:

set y = 0

0 = -2x - 1

2x = -1

x = -1/2

Then take the second derivate by taking the derivative of the first derivative (

Because the result is negative, we know that the graph faces downward like a frowning face.

To solidify this answer, take a look at the graph. graph{-x^2 - x + 4 [-10, 10, -5, 5]}