Next, we need to find the points of intersection of the two curves, which we do by setting them
equal to each other and solving for x.
x^2 = 6x − x^2
2 x^2 = 6x
2 x^2 − 6x = 0
2 x(x − 3) = 0
x = 0 or x = 3
We can find the area between the two curves by integrating the top curve minus the bottom
curve, using the points of intersection as the limits of integration. We get
[(6x − x^2 ) − (x^2 )] dx
We evaluate the integral and we get [(6x − 2x^2 ) dx = = 9.
- D A function is decreasing on an interval where the derivative is negative.
The derivative is f′(x) = 4x^3 + 12x^2.
We want to determine on which intervals the derivative of the function is positive and on which
it is negative. We do this by finding where the derivative is zero.
