simple rates of change (1 Viewer)

[atakach99]

For a certain graph, the rate of change of y values with respect to its x values is given by R= 3x^2 - 2x +1. If the graph passes through the point (-1,3), find its equation.

 

[lyounamu]

For a certain graph, the rate of change of y values with respect to its x values is given by R= 3x^2 - 2x +1. If the graph passes through the point (-1,3), find its equation.

R = 3x^2 - 2x + 1
y = x^3 - x^2 + x + c (by integration of R)
Since the graph passes through the point (-1,3), substituting x = -1 and y=3 should satisfy the equation.
3 = (-1)^3 - (-1)^2 + -1 + c
3 = -1 -1 -1 + c
c = 6
Therefore, y = x^3 -x^2 + x + 6