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| Forum Index -> Differential Calculus -> View Full Question |
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Consider the function f(x) = x^2 - xsinx - cosx f'(x) = 2x -xcosx = x(2-cosx) f'(x) is increasing for x>0 and decreasing for x<0
Now f(0) = -1 f(- infinity) = +infinity This is a continuous function for obvious reasons.So from - inf to 0, f(x) crosses x axis once and since it increase after 0 it also crosses it again. Hence exactly 2 roots.
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