Question

At each point (x,y) on the curve the slope is 2x+3 the curve passes through the point (-3,0)

Answer 1

The equation of the curve is y = x² + 3x

Explanation:

I get your drift, but wish you had stated specifically that you wanted to find the equation of this curve.

Slope of tangent line to curve is dy/dx = 2x + 3.

Integrating that with respect to x yields y = x² + 3x + C.

The point (-3, 0) must satisfy this equation:

0 = (-3)² + 3(-3) + C, so C = 0.

The equation of the curve is y = x² + 3x