Use the intermediate Value Theorum to prove that f(x)=x^3 -9x +5 has a real zero in...
Use the intermediate Value Theorum to prove that f(x)=x^3 -9x +5 has a real zero in each of the following intervals [-4,-3], [0,1], and [2,3] (show work)
Homework Answers
f(x) = x^3 - 9x + 5
[ - 4 , - 3 ]
f(-4) = (-4)^3 - 9 (-4) + 5 = - 23
f(-3) = (-3)^3 - 9 (-3) + 5 = 5
as f(-4) is negative and f(-3) is positive
according to intermediate value theorem
there exists a zero in the interval [ -4 , - 3]
[ 0 , 1 ]
f(0) = 5
f(1) = - 3
as f(1) is negative and f(0) is positive
according to intermediate value theorem
there exists a zero in the interval [ 0 , 1 ]
[ 2 , 3 ]
f(2) = (2)^3 - 9 (2) + 5 = - 5
f(3) = (3)^3 - 9 (3) + 5 = 5
as f(2) is negative and f(3) is positive
according to intermediate value theorem
there exists a zero in the interval [ 2 , 3 ]
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