The equation of the curve whose slope at point (x, y) is x^2-2 and which contains the point (1 -3) is

Question

A) y= 1/3x^3-2x

B) y=2x-1

C) y= 1/3x^3-10/3

D) y=1/3x^3-2x-4/3

E) 3y= x^3-10

Answer 1

We have y' = x² - 2; y = ∫(x² - 2)dx = x³/3 - 2x + C.

We use point (1, - 3): - 3 = 1/3 - 2 + C; C = - 4/3.

So, y = x³/3 - 2x - 4/3

Answer is D)