Posted by UCI STUDENT on Wednesday, January 25, 2012 at 6:36pm.
Use the Intermediate Value Theorem to check whether the equation x^3–3x+2.1=0 has a root in the interval (0,1)
answer: yes or no ?
i have no idea how to answer to go about solving this question, thanks for the help!

Calc  Damon, Wednesday, January 25, 2012 at 7:44pm
if x = 0 the function is 2.1
if x = 1 , the function is 0.1
so it does not necessarily cross the x axis between those points
If it does cross, it must cross twice to go from + to  to + again
so it would have to have a slope of zero in between there
df/dx = 3 x^2 3
0 = x^2  1
x= +1 or 1 for 0 slope
so it has no zero slope points between 0 and 1
So
It never crosses the x axis between 0 and 1
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