Question

Find the absolute extreme f(x)=x square defined on [-2,2]

Answer 1

Answer:

Step-by-step explanation:

Finding absolute extrema on a closed interval

Extreme value theorem tells us that a continuous function must obtain absolute minimum and maximum values on a closed interval. These extreme values are obtained, either on a relative extremum point within the interval, or on the endpoints of the interval.

Let's find, for example, the absolute extrema of h(x)=2x^3+3x^2-12xh(x)=2x  

3

+3x  

2

−12xh, left parenthesis, x, right parenthesis, equals, 2, x, cubed, plus, 3, x, squared, minus, 12, x over the interval -3\leq x\leq 3−3≤x≤3minus, 3, is less than or equal to, x, is less than or equal to, 3.

h'(x)=6(x+2)(x-1)h  

′

(x)=6(x+2)(x−1)h, prime, left parenthesis, x, right parenthesis, equals, 6, left parenthesis, x, plus, 2, right parenthesis, left parenthesis, x, minus, 1, right parenthesis, so our critical points are x=-2x=−2x, equals, minus, 2 and x=1x=1x, equals, 1. They divide the closed interval -3\leq x\leq 3−3≤x≤3minus, 3, is less than or equal to, x, is less than or equal to, 3 into three parts:

Similarily, do for [-2,2]

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