Question 1201980: Find the maximum value of y = x3 - 2x2 + x - 2 on the horizontal span from 2 to 5.
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
ANSWER: 78 (at x=5)
method 1: use a graphing calculator (or some other graphing utility) to see that the function is increasing everywhere on the given interval.
method 2: use algebra to factor the polynomial as (x^2+1)(x-2); then, since x^2+1 is always positive, you know that the function is increasing everywhere to the right of x=2.
method 3: use calculus to find the derivative is 3x^2-4x+1 = (3x-1)(x-1), telling you that the zeros of the derivative are at x=1/3 and x=1, and that therefore the function is increasing everywhere to the right of x=1, which means it is increasing everywhere on the given interval.
And there are undoubtedly other methods....
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