Math 115 HW #8 Solutions

(a) y′ = 1 + xy (b) y′ = −2xy (c) y′ = 1− 2xy Answer: If (b) were correct, then, when x = 0, we would have that y′ = 0. However, the slope of the tangent line is clearly positive when x = 0 in the picture, so (b) cannot be correct. If (a) were correct, then y′ would be positive for all positive values of x. However, the slope of the tangent line is clearly negative for most positive x, so (a) cannot be correct. Thus, (c) must be the equation which is solved by the function whose graph we see.