Find the number(s) c referred to in the intermediate valuetheorem for the function over the interval indicated and for thegiven value of L. f(x)=-x^2 +2x+3 over [-1, 0] using L=2.

ganolrifv9 2022-07-27 Answered
Find the number(s) c referred to in the intermediate valuetheorem for the function over the interval indicated and for thegiven value of L.
f ( x ) = x 2 + 2 x + 3 over [-1,0] using L = 2.
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Answers (1)

Danica Ray
Answered 2022-07-28 Author has 15 answers
intermediate value theorem: Iff is continuous on a closed interval [a,b] and L is any number between f(a) andf(b) then there is at least one number c in [a,b] such that f(c) = L.
f ( b ) = ( 1 ) 2 + 2 ( 1 ) + 3 = 0
f(a) = 0 + 0 + 3 = 3
L = 2 so it is between f(b) and f(a)
x 2 + 2 x + 3 = 2
x 2 + 2 x + 1 = 0
Use quadratic formula to solve: x or c = 2.4142, which is on theinterval.
(double check: ( 2.4142 ) 2 + 2 ( 2.4142 ) + 3 = 2.0000)

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