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AP Calculus

AP Calculus

memorize.aimemorize.ai (lvl 286)
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Section 1

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Alternate definition of derivative

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6 years ago

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Mar 1, 2020

Cards (14)

Section 1

(14 cards)

Alternate definition of derivative

Front

limit as x approaches a of [f(x)-f(a)]/(x-a)

Back

Squeeze Theorem

Front

if f(x)≤g(x)≤h(x) for all numbers, and at some point x=k we have f(k)=h(k), then g(k) must also be equal to them.

Back

d/dx cos(x)

Front

-sinx

Back

Continuity

Front

1. the function is defined at the point. 2. the function has a limit from that side at that point. 3. the one-sided limit equals the value of the function at the point.

Back

Lim x approaches 0 sin(x)/x

Front

1

Back

First Derivative Test

Front

1. f'(x) changes from Negative to postive at c, then f has a relative min at (c, f(c)) 2. if f'(x) changes from Positive to Negative at c the f has a relative max at (c,f(c)) 3. if f'(x) is positive or negative on both sides of c then c is neither max nor min

Back

d/dx [x^n] (Power Rule)

Front

nx^n-1

Back

Lim x approaches infinity sin(x)/x

Front

0

Back

Extreme Value Theorem (EVT)

Front

If f is continuous on a closed interval [a,b], then f has both a minimum and a maximum on the interval.

Back

Rolle's Theorem

Front

Let f be continuous on [a,b] and differentiable on (a,b) and if f(a)=f(b) then there is at least one number c on (a,b) such that f'(c)=0 (If the slope of the secant is 0, the derivative must = 0 somewhere in the interval).

Back

Definition of Derivative

Front

Back

d/dx(sinx)

Front

cos(x)

Back

Intermediate Value Theorem (IVT)

Front

If f is continuous on [a,b] and k is any number between f(a) and f(b), then there exists at least one number c such that f(c)=k

Back

Mean Value Theorem

Front

if f is continuous on [a,b] and fdifferentiable there exist C such that f′(c)=f(b)−f(a)/b−a

Back