A curve y=f(x) has a gradient dy/dx=2x - 3x^2

Question

Find the coordinates of the point on the curve where x=3 How do I fint the coordinates?

Answer 1

Given Curve y = f(x) 

dy/dx = 2x - 3x²

Multiply each side by dx .

dy = (2x - 3x² )dx

Integrate each side .

Ignore the constant term in this case .

When x = 3 the value y is 

y = (3)² - (3)³ ⇒ 9 - 27 = -18 

Hence the coordinates of the point on the curve is (3,-18)