Question

$f\left(x\right)=-3x^2+2x+5$ is concave at

• A. 3
• B. 2
• C. 1
• D. -2

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A

3

B

2

C

1

D

-2

In the interval in which a function is concave, the value of the derivative f’(x) keeps on reducing. So we can say f”(x) will be less than zero.

Let’s double differentiate the given function.

$f\left(x\right)=-3x^2+2x+5$

f’(x) = - 6x + 2

f”(x) = - 6

Here, we get the second derivative to be negative for all the values of x. So we can say that the function is concave at all the points given.