Question

Find a and b such that f is differentiable everywhere...

Options:
A. f(x) = ax² + b
B. f(x) = e(ax + b)
C. f(x) = ln(ax + b)
D. f(x) = sin(ax + b)

Answer 1

The function that satisfies the given conditions is f(x) = ax² + b. We can choose values for a and b to meet the conditions.

Step-by-step explanation:

The function that satisfies the given conditions is option A. f(x) = ax² + b.

To be differentiable everywhere, a function must be continuous and have a derivative at each point. Option A represents a quadratic function, which is continuous and differentiable everywhere. So, we can choose values for a and b such that the function satisfies the conditions.

For example, let's say we choose a = 1 and b = 0. The function becomes f(x) = x², which is a quadratic function with positive value at x = 3 and a positive slope that decreases in magnitude with increasing x.