AP Calculus ABeasymcq1 pt

If a function $f$ is differentiable at $x=a$ , which of the following must be true?

f(a)=0

f

has a corner at

x=a

f

is increasing near

x=a

f

is continuous at

x=a

Explanation

Core Concept

Differentiability requires the limit $\lim\limits_{h\to 0}\dfrac{f(a+h)-f(a)}{h}$ to exist, which forces $\lim\limits_{x\to a}f(x)=f(a)$ . So differentiability implies continuity, but not the converse.

Correct Answer

D $f$ is continuous at $x=a$

More Unit 2: Differentiation: Definition and Basic Derivative Rules practice questions

hardIf $f(x)=\dfrac{\cos x}{x^2}$, then $f'(x)=$
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Practice Unit 2: Differentiation: Definition and Basic Derivative Rules Questions →

If a function fff is differentiable at x=ax=ax=a, which of the following must be true?

Explanation

Core Concept

Correct Answer

More Unit 2: Differentiation: Definition and Basic Derivative Rules practice questions

If a function $f$ is differentiable at $x=a$ , which of the following must be true?