![y=x^5-3\\ y'=5x^4\\\\ 5x^4=0\\ x=0\\ 0\in [-2,1]\\\\ y''=20x^3\\\\ y''(0)=20\cdot0^3=0](/tpl/images/0175/9691/0e2bd.png)
is neither positive nor negative, so you can't tell whether this point is a minimum or a maximum. You need to check the values of the first derivative around the point.
is always positive for 
. That means at ![[-2,1]](/tpl/images/0175/9691/cf9ae.png)
.
is increasing in its entire domain, so the maximum value is at the right endpoint of the interval.
Ex 2.8
3. find the maximum value of y for the curve y=x^5 -3 for -2≤x≤1...
Mathematics, 18.08.2019 11:50 davisdarby2
Ex 2.8
3. find the maximum value of y for the curve y=x^5 -3 for -2≤x≤1
Answers: 1
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