Ex 2.8
3. find the maximum value of y for the curve y=x^5 -3 for -2≤x≤1

Answers

Answer 1

Answer: $y=x^5-3\n y'=5x^4\n\n 5x^4=0\n x=0\n 0\in [-2,1]\n\n y''=20x^3\n\ny''(0)=20\cdot0^3=0$

The value of the second derivative for $x=0$ 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.
But the value of $5x^4$ is always positive for $x\in\mathbb{R}\setminus \{0\}$ . That means at $x=0$ there's neither minimum nor maximum.
The maximum must be then at either of the endpoints of the interval $[-2,1]$ .
The function $y$ is increasing in its entire domain, so the maximum value is at the right endpoint of the interval.

$y_(max)=y(1)=1^5-3=-2$

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Answers

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i think this answer will help you

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Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answers

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