The curve passes through the origin.

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

The curve sin⁡(xy)+y=x\sin(xy)+y=x passes through the origin. (a) Calculate dydx\dfrac{dy}{dx} at the point (0,0)(0,0). (b) Determine d2ydx2\dfrac{d^{2}y}{dx^{2}} at (0,0)(0,0). (c) Using the value found in part (b), state whether the curve is concave up, concave down, or neither in a neighborhood of the origin, and justify your conclusion.

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