Answer:
the correct answer is option C because it is maximum at (0,-2)
Step-by-step explanation:
given equation,
y = -x² -2
to find maxima and minima we will differentiate the equation
![\frac{\mathrm{d} y}{\mathrm{d} x}=-x^2-2](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20y%7D%7B%5Cmathrm%7Bd%7D%20x%7D%3D-x%5E2-2)
![\frac{\mathrm{d} y}{\mathrm{d} x}=-2x\\\frac{\mathrm{d} y}{\mathrm{d} x}=-2](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20y%7D%7B%5Cmathrm%7Bd%7D%20x%7D%3D-2x%5C%5C%5Cfrac%7B%5Cmathrm%7Bd%7D%20y%7D%7B%5Cmathrm%7Bd%7D%20x%7D%3D-2)
hence we can see that double differentiation is - ve so the equation will maximum.
hence, now putting value from option C
the value of y comes out to be -2
now, putting value from option D
value of y comes out to be -6
hence, the correct answer is option C because it is maximum at (0,-2)