2x - 1, x<1 x2, x > 1 1. Given the function f(x) = Which of the following statements is/are true? A. f is continuous and differentiable for all x. B. f is continuous but not differentiable at x = 1. C. f'(x) = 2 for all x. D. f'(x) = 2x for all x. %3D

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A: Explanation of the answer is as follows

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: