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AP Calculus

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Section 1

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Intermediate Value Theorem (IVT)

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Calculus Math

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Mar 1, 2020

Cards (18)

Section 1

(18 cards)

Intermediate Value Theorem (IVT)

Front

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

Back

Mean Value Theorem

Front

if f(x) is continuous and differentiable, slope of tangent line equals slope of secant line at least once in the interval (a, b) f '(c) = [f(b) - f(a)]/(b - a)

Back

Vertical asymptote of a function

Front

occurs at x value which makes denominator 0

Back

acceleration function

Front

Derivative of velocity function a(t) = v'(t) = s''(t)

Back

Critical point of a function

Front

f'(x) = 0 or undefined

Back

instantaneous rate of change

Front

Derivative (slope of tangent line)

Back

f(x) has a local minimum

Front

f'(x) changes from negative to positive

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

f(x) is concave down

Front

f''(x) is negative f'(x) is decreasing

Back

f(x) is concave up

Front

f''(x) is positive f'(x) is increasing

Back

f(x) is decreasing

Front

f'(x) is negative

Back

average rate of change of f(x) on [a, b]

Front

f(b)-f(a)/b-a the slope of the secant line from x=a to x=b

Back

f(x) is increasing

Front

f'(x) is positive

Back

How to find horizontal asymptotes

Front

limit as x approaches infinity and negative infinity

Back

velocity function

Front

Derivative of Position Function v(t) = s'(t)

Back

f(x) has a local maximum

Front

f'(x) changes from positive to negative

Back

f(x) is differentiable

Front

f'(x) is defined

Back

f(x) has a point of inflection

Front

f''(x) changes from + to - or - to + at a defined point

Back