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Question 813352: please help:
show that there is at least one function to x^3+x=3 for x greater than 0.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! I assume you mean there is at least one solution (zero) of the function for x>0?
To show that the function has a zero, we can use the intermediate value theorem.
This states that if a function f(x) is continuous and f(x) < 0 at a point a and f(x) > 0 at a point b,
then there must be a zero at some point, c, in between a and b.
x^3+x = 3 -> x^3+x-3
f(x) = x^3+x-3
f(1) = 1+1-3 = -1
f(2) = 8+2-3 = 9
This means that the function crosses zero on the interval (1,2)
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