Find the maximum value of y in the equation y = 1 – 2x – 3x(^2)
-
A.
5/4 -
B.
5/3 -
C.
3/4 -
D.
4/3
Correct Answer: Option D
Explanation
(y = 1 – 2x – 3x^2)
At maximum point, (frac{mathrm d y}{mathrm d x} = 0)
(frac{mathrm d y}{mathrm d x} = -2 – 6x)
(-2 – 6x = 0 implies -2 = 6x)
(x = -frac{1}{3})
At x = (-frac{1}{3}), y = (1 – 2(-frac{1}{3}) – 3(-frac{1}{3})^{2})
= (1 + frac{2}{3} – frac{1}{3})
= (frac{4}{3})