Question

how to determine if a function is differentiable at a point

Answer 1

Answer:

In order for a function to be differentiable at a point, it must be continuous at that same point.

General Formulas and Concepts:

Calculus

Continuity

• f(c) exists
• $\displaystyle \lim_{x \to c} f(x)$  exists
• $\displaystyle f(c) = \lim_{x \to c} f(x)$  

Discontinuities

• Removable (Hole)
• Jump
• Infinite (Asymptote)

Differentiation

• Derivatives

Step-by-step explanation:

In order for a function to be differentiable, it must be continuous. That means that the function must have a limit that exists and that it should not contain discontinuities.

If the function contains discontinuities, then the function is not continuous at the discontinuities and therefore is not differentiable there.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation