Find the point on the graph of y = x^2 where the curve has slope m = -18.

Question

The point is ________ (Type an ordered​ pair).

Answer 1

y = x² is our function of interest. It's a quadratic with an upwards U parabolic shape — this means it's decreasing and has negative slope values from (-∞, 0).

If we differentiate the function of interest, we'll get the rate of change with respect to x or slope. We can use the power rule:

dy/dx = 2*x^2-1 → 2x¹→ 2x.

dy/dx = -18 → 2x = -18 → x = -9.

To report this result as an ordered pair, plug -9 into our original function:

y(-9) = (-9)² = 81 → (-9, 81).