Question

The second derivative of the function f

Answer 1

According to it's second derivative, the function has points of inflection given by:

Answer B: 1 and 2.467.

What are the points of inflection of a function?

The points of inflection of a function are the values of x for which:

$f^{\prime\prime}(x) = 0$

In this problem, the second derivative is:

$f^{\prime\prime}(x) = x^2\cos{(\sqrt{x})} - 2x\cos{(\sqrt{x})} +\cos{(\sqrt{x})}$

Hence:

$x^2\cos{(\sqrt{x})} - 2x\cos{(\sqrt{x})} +\cos{(\sqrt{x})} = 0$

$(x^2 - 2x + 1)\cos{(\sqrt{x})} = 0$

$x^2 - 2x + 1 = 0 \rightarrow (x - 1)^2 = 0 \rightarrow x = 1$

$\cos{(\sqrt{x})} = 0$

$\sqrt{x} = \frac{\pi}{2}$

$(\sqrt{x})^2 = \left(\frac{\pi}{2}\right)^2$

$x = 2.467$

Hence option B is correct.

You can learn more about points of inflection at brainly.com/question/10352137