Derivatives and Continuity Quiz

What is the definition of derivative?

• The slope of a tangent line to a curve at a given point

• The area under a curve

• The integral of a function

• The limit of a function

A function is continuous at a point if:

• The function is defined at that point

• The function has a vertical asymptote at that point

• The function has a removable discontinuity at that point

• The limit of the function exists at that point and is equal to the value of the function

Which of the following statements is true about limits and continuity?

• If a function is continuous at a point, then the limit of the function at that point exists

• If the limit of a function at a point exists, then the function is continuous at that point

• Limits and continuity are unrelated concepts

• None of the above

A function is differentiable at a point if:

• The function is continuous at that point

• The function has a vertical asymptote at that point

• The function has a removable discontinuity at that point

• The derivative of the function exists at that point

Which of the following functions is not differentiable at x = 0?

• f(x) = |x|

• f(x) = x^2

• f(x) = sin(x)

• f(x) = 1/x

If a function is differentiable at a point, then it is also:

• Continuous at that point

• Discontinuous at that point

• Undefined at that point

• None of the above

Which of the following functions is continuous on its entire domain?

• f(x) = x^2

• f(x) = 1/x

• f(x) = sin(x)

• f(x) = |x|

The derivative of a constant function is always:

• Zero

• One

• Infinity

• Undefined

Which of the following functions is not differentiable on its entire domain?

• f(x) = x^2

• f(x) = 1/x

• f(x) = sin(x)

• f(x) = |x|

If a function is differentiable at a point, then it is also:

• Continuous at that point

• Discontinuous at that point

• Undefined at that point

• None of the above