Answer:
D.
Step-by-step explanation:
that is the answer to the question above
![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](https://tex.z-dn.net/?f=y%3Dx%5E5-3%5C%5C%20y%27%3D5x%5E4%5C%5C%5C%5C%205x%5E4%3D0%5C%5C%20x%3D0%5C%5C%200%5Cin%20%5B-2%2C1%5D%5C%5C%5C%5C%20y%27%27%3D20x%5E3%5C%5C%5C%5C%0Ay%27%27%280%29%3D20%5Ccdot0%5E3%3D0)
The value of the second derivative for
![x=0](https://tex.z-dn.net/?f=x%3D0)
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](https://tex.z-dn.net/?f=5x%5E4)
is always positive for
![x\in\mathbb{R}\setminus \{0\}](https://tex.z-dn.net/?f=x%5Cin%5Cmathbb%7BR%7D%5Csetminus%20%5C%7B0%5C%7D)
. That means at
![x=0](https://tex.z-dn.net/?f=x%3D0)
there's neither minimum nor maximum.
The maximum must be then at either of the endpoints of the interval
![[-2,1]](https://tex.z-dn.net/?f=%5B-2%2C1%5D)
.
The function
![y](https://tex.z-dn.net/?f=y)
is increasing in its entire domain, so the maximum value is at the right endpoint of the interval.
Cross multiplying we get
x^2 = 2*7x
x^2 = 14x
x^2 - 14x = 0 is the answer