If f is differentiable at the point a, which statement must be true?

• f is continuous at a
• f has a corner at a
• f is constant near a
• f has a vertical tangent at a

If f is differentiable at the point a, which statement must be true?

• f is continuous at a
• f has a corner at a
• f is constant near a

Which function is continuous at 0 but not differentiable at 0?

• f(x) equal to x squared
• f(x) equal to the absolute value of x
• f(x) equal to 2x plus 1

Priya claims: if f is differentiable at a, then the limit of f(x) as x tends to a equals f(a). Is Priya right?

Circle one:   True   False

Sam says every continuous function is differentiable at every point. Is Sam right?

Circle one:   True   False

Let f(x) equal to x squared on [0, 4]. The mean value theorem gives c with f prime of c equal to the secant slope. What is c? Give a decimal.

Answer: ______________

Sam says every continuous function is differentiable at every point. Is Sam right?

Circle one:   True   False

Priya claims: if f is differentiable at a, then the limit of f(x) as x tends to a equals f(a). Is Priya right?

Circle one:   True   False

A student proves differentiability implies continuity by writing the output change as quotient times input change. A friend objects that the quotient might not exist. What settles it?

• Continuity must be assumed first
• Differentiability means exactly that the quotient limit exists and equals the derivative
• The input change is always zero

Let f(x) = x squared on the interval from 0 to 4. The mean value theorem says some c between 0 and 4 has f'(c) equal to the secant slope. What is c? Give your answer as a decimal.

Answer: ______________