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26.06.2019 •
Mathematics
Verify that the function satisfies the three hypotheses of rolle's theorem on the given interval. then find all numbers c that satisfy the conclusion of rolle's theorem. (enter your answers as a comma-separated list.) f(x) = 4x2 − 8x + 3, [−1, 3] c =
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Ответ:
Rolle's Theorem states that:
If f is a continuous function in [a,b] and is differentiable in (a,b)
such that f(a)=f(b)
Then there exist a constant c in between a and b i.e. c∈[a,b]
such that: f'(c)=0
Here we have the function f(x) as:
where x∈[-1,3]
Since the function f(x) is a polynomial function hence it is continuous as well as differentiable over the interval [-1,3].Also,
f(-1)=15
(Since,
and f(3)=15
( Since,
)
i.e. f(-1)=f(3)Hence, there will exist a c∈[-1,3] such that f'(c)=0
Hence, the c that satisfy the conclusion is: c=1
Ответ:
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