Question

bonus 1pt true or false: a function is differentiable at a corner. bonus 1pt true or false: a function is not differentiable at a vertical tangent.

Explanation:

First Question (A function is differentiable at a corner)

To determine differentiability at a corner, recall the definition of the derivative as the limit of the difference quotient. At a corner, the left - hand derivative (the slope of the tangent from the left) and the right - hand derivative (the slope of the tangent from the right) exist but are not equal. Since the derivative at a point exists only when the left - hand and right - hand derivatives are equal, a function is not differentiable at a corner. So the answer is False.

For a vertical tangent, the slope of the tangent line is undefined (it approaches $\pm\infty$). The derivative of a function at a point represents the slope of the tangent line at that point. If the slope of the tangent is undefined, then the derivative does not exist at that point. So a function is not differentiable at a vertical tangent, and the answer is True.

Answer:

False

Second Question (A function is not differentiable at a vertical tangent)