What is the complete set of numbers for which f(x) = x3 + 2x2 - x is concave?

Concave up at

Concave down at

Step-by-step explanation:

The given function is

In order to check the concavity, we find the inflection point. To find inflection point we calculate the second derivative of the function and then equate it to zero.

The first derivative is given by

The second derivative is given by

For inflection point

Hence, the inflection point is

Hence, on the left of   the curve is concave downward and on the right of   the curve is concave up.

Hence,

Concave up at

Concave down at

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2