Question

Let y=f(x) be a twice-differentiable function such that f(1)=2.

A) f'(1) represents the rate of change at x=1
B) f''(1) denotes the concavity at x=1
C) The function is not differentiable
D) f(1) is equal to the y-intercept

Answer 1

f''(1) denotes the concavity at x=1.

Step-by-step explanation:

A) f'(1) represents the rate of change at x=1.

B) f''(1) denotes the concavity at x=1.

C) The function is not differentiable.

D) f(1) is equal to the y-intercept.

In this case, since y=f(x) is a twice-differentiable function and f(1)=2, we can conclude that option B is correct. f''(1) denotes the concavity at x=1. This means that at x=1, the graph of the function has concavity, which helps us determine the shape of the graph in the vicinity of x=1.