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Calculus Theorems

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Section 1

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Extreme Value Theorem

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Calculus Math

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Mar 14, 2020

Cards (9)

Section 1

(9 cards)

Extreme Value Theorem

Front

Back

Rolle's Theorem

Front

Back

Intermediate Value Theorem

Front

Back

Mean Value Theorem

Front

Back

Intermediate Value Theorem

Front

If f(x) is continuous on [a,b] and f(a)<y< f(b) or f(b)<y<f(a) then there is at least one value of c on (a,b) such that f(c)= y

Back

Fundamental Theorem of Calculus

Front

Back

Extreme Value Theorem

Front

If f(x) is continuous on [a,b] then there must be an absolute max AND absolute min on the interval {a,b]. These absolute extrema can occur at x=a x=b (endpoints) or any critical point of f on [a,b].

Back

Rolle's Theorem

Front

If f(x) is continuous on [a,b] AND differentiable on (a,b) AND f(a)=f(b) , then there is guaranteed a value of c on (a,b) such that f'(c)=0.

Back

Mean Value Theorem

Front

If f(x) is continuous on [a,b] and differentiable on (a,b), then there is guaranteed to be a value of c on (a,b) such that f'(c)= f(a)-f(b)/a-b --secant

Back