9.1 - Calculus - Random Derivative Stuff

If a function is continuous at a point, then it is differentiable at that point.

• True

• False

If a function is differentiable at a point, then it is continuous at that point.

• True

• False

The slope of a function is described by its ____________.

• first derivative

• second derivative

• third derivative

• expression

Tags

CCSS.HSF.IF.B.6

Is the above function differentiable for all values of x? Why?

• Yes, the slope of the tangent line can be calculated for all values of x.

• Yes, the function is continuous for all values of x so the function is differentiable.

• No, the function has a sharp turn in the first quadrant so if is not differentiable.

• No, the function is discontinuous so it is not differentiable.

In which quadrant of the graph above will there be a value of x that is non-differentiable?

• 1

• 2

• 3

• 4

Tags

CCSS.8.F.A.3

Which of the following would be a valid reason the above function is non-differentiable at x = 0?

• The graph contains a corner.

• The graph contains a cusp.

• The graph contains a discontinuity.

• The graph contains a vertical tangent.

Tags

CCSS.8.F.A.3

If  $f\left(x\right)$  has a derivative at x = a, then f is continuous at x = a.

• True

• False

Where is the graph not differentiable?

• x = -2, -1, 0, 1

• x = -2, -1, 1

• x = -2, -1

• x = -1,

A function whose graph is otherwise continuous will fail to have a derivative at a point where the graph has a...

• corner, horizontal tangent, discontinuity

• corner, vertical tangent, continuity

• corner, vertical tangent, discontinuity

• corner, vertical tangent, continuity

What is the derivative of cot(x)?

• sec²(x)
• -sec²(x)
• csc²(x)
• -csc²(x)