Question

a point moves on the parabola y=x^2 so that is abscissa increases at rate of 3 feet per second what rate is the ordinate increasing when x=2

ans;12 ft /sec

Answer 1

looks good

Answer 2

y = x²

dy / dx = 2 x

Multiply both sides by dx

dy = 2 x dx

Divide both sides by dt

dy / dt = 2 ∙ x ∙ dx / dt

Abscissa increases at rate of 3 feet per second means: dx / dt = 3 ft / s

dy / dt = 2 ∙ x ∙ dx / dt

for x = 2

dy / dt = 2 ∙ 2 ∙ 3 = 12 ft / s