Asked by David
a) prove that the function x^3 + 9x^2 +33x assumes the value -8 at least once
b)using the mean value theorom or rolle's theorom - no other methods will be accepted - prove carefully that x^3 + 9x^2 + 33x takes on the value -8 at most once
b)using the mean value theorom or rolle's theorom - no other methods will be accepted - prove carefully that x^3 + 9x^2 + 33x takes on the value -8 at most once
Answers
Answered by
MathMate
a.
determine the domain and range of the function and conclude.
b.
Prove by contradiction:
assume that there are two or more values of x for which f(x1)=-8 and f(x2)=-8, where x1<x2.
Consider the interval [x1,x2], and apply Rolle's theorem or the mean value theorem to see if it is possible to find such x1, x2.
determine the domain and range of the function and conclude.
b.
Prove by contradiction:
assume that there are two or more values of x for which f(x1)=-8 and f(x2)=-8, where x1<x2.
Consider the interval [x1,x2], and apply Rolle's theorem or the mean value theorem to see if it is possible to find such x1, x2.
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