f(x)= – x2f′′(x)=

Answer 1

The function given is (f(x) = -x^2). The second derivative of a function, denoted as (f’'(x)), measures the concavity of the function.

For the function (f(x) = -x^2), the first derivative (f’(x)) is (-2x).

Taking the derivative of (f’(x)) gives us the second derivative (f’‘(x)), which is (-2). So, (f’'(x) = -2). This indicates that the function (f(x) = -x^2) is concave down for all (x), because the second derivative is negative.