Which of the following functions is differentiable everywhere?
Correct Answer: f(x) = x^2
- Step 1: Understand what differentiable means. A function is differentiable at a point if it has a defined slope (derivative) at that point.
- Step 2: Know that polynomials are functions made up of terms like x^n, where n is a non-negative integer.
- Step 3: Recognize that polynomials, like f(x) = x^2, are smooth and continuous everywhere on the graph.
- Step 4: Conclude that since f(x) = x^2 is a polynomial, it is differentiable at every point on the graph.
No concepts available.
