Question

Question 5 of 10 Suppose f(x)=−x21​. Then f′′(x)= A. −x−33​ B. −21​x−23​ C. 41​x−23​ D. 21​x−23​ E. −41​x−23​

Answer 1

To find the second derivative of the function f(x) = -x^2/1, we need to differentiate it twice.

Step 1: Find the first derivative of f(x):

Using the power rule of differentiation, we get:

f'(x) = -2x^(2-1)/1

= -2x^1

= -2x

Step 2: Find the second derivative of f(x):

Differentiating f'(x), we get:

f''(x) = d/dx (-2x)

= -2

Therefore, the second derivative of f(x) is a constant, -2.

None of the options A, B, C, D, or E match our result of -2. Hence, none of the provided options is correct for the second derivative of f(x).