$f (x) = - 3 x^{2} + 2 x + 5$ is concave at

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-2

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Solution

The correct option is 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.

$f (x) = - 3 x^{2} + 2 x + 5$

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.

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Similar questions

$f (x) = - 3 x^{2} + 2 x + 5$ is concave at

f (x) = - x^{3} + 3 x^{2} - 2 x + 2

f (x) = 3 x^{2} - 2 x + 5

lim x \to 0 \frac{f (x + h) (- f (x)}{h}

f (x) = 3 x^{2} - 2 x - 5

f (x) = \sqrt{\frac{2 x + 1}{x^{3} - 3 x^{2} + 2 x}}

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