Continuities and Derivatives Flashcards Preview

AP Calculus AB > Continuities and Derivatives > Flashcards

Flashcards in Continuities and Derivatives Deck (8)
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1
Q

Only discontinuous if

  • There is no _ (asymptote)
  • _ (LHL!=RHL)
  • lim(x->a) != _
A

Y value, DNE, f(a)

2
Q

Three steps to prove _

  • LHL
  • RHL
  • LHL=RHL
A

Continuous

3
Q

Intermediate Value Theorem

  • Plug in [] in f(x) to get ()
  • By the intermediate value theorem, since 0 is between (y range) there is a root on the interval [x range]
A

X range, y range

4
Q

Derivatives

  • Plug in f’(x) = lim(h->0) [f(x+h) – f(x)] / h into _
  • Simplify
  • Cancel h
  • Plug in _ for h
A

f(x), 0

5
Q

Solve for f’(a)

  • Plug in _ in f’(x) for x
  • Plug in f’(x) in _
  • Simplify
  • Cancel h
  • Plug in 0 for h
A

a, f(x)

6
Q

Alternate _

  • Plug in a into f’(a) = lim(x->a) [f(x) – f(a)] / (x-a)
  • Cancel
A

f’(a)

7
Q

Graphing slope of f’(x)

  • _
  • Plot + and –
  • Plot _
  • Graph slope
A

Arrows, 0

8
Q

Prove continuous on (-infinity, infinity)

  • lim(x->n+) = _
  • Solve
A

lim(x->n-)