Question

Determine the slope of y=3x^2-8 at (x,y)

Answer 1

By definition, the slope of a curve is the rate of change of the independent and dependent variables. When graphed in a Cartesian plane, the slope between any two point on the curve is equal to Δy/Δx. However, we should not that only a linear function has a constant slope. For this problem, the equation is quadratic. Hence, you must specify the point where we should get the slope.

In calculus, the slope is the first derivative of the equation:

y=3x²-8
dy/dx = slope = 6x - 0

Thus, the slope at any point of the curve is 6x. For instance, you want to find the slope of the curve at point (1,1), then the slope is equal to 6(1) = 6 units.