Continuity and Differentiability

One of the conditions a function must satisfy to be continuous at x=c is "f(c) must exist"

• TRUE

• FALSE

Tags

CCSS.HSF.BF.B.3

A function is continuous on a number if and only if f(c) = lim f(x) as x approaches a number c.

• TRUE

• FALSE

Which of the following best describes the continuity at x = 1?

• Continuous

• Removable Discontinuity

• Infinite Discontinuity

• Jump Discontinuity

Tags

CCSS.HSF-IF.C.7B

Find the value of b for which g(x) is continuous at x=3.

Is the above function differentiable at x = 0? Why?

• No. The undefineddoesn't exist since the left and right hand limits are not the same.

Is the above function differentiable at

x = 0? Why?

• Yes. The derivative would be equal to zero since there is a vertical tangent.

• No. The derivative would not exist at x = 0 since there is a vertical tangent.

• True

• False

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

• corner, cusp, horizontal tangent, discontinuity
• corner, cusp, vertical tangent, continuity
• corner, cusp, vertical tangent, discontinuity
• corner, curve, vertical tangent, continuity

Is the function continuous, differentiable, both, or neither?

• continuous

• differentiable

• both

• neither

Tags

CCSS.HSF-IF.C.7B

Find the values of a and b that make the function f differentiable.