(−0.786, 4.209).
Graphing Calculator (TI-83 and TI-84)
Press the Y= button, and enter the following values to the list:
Y 1 = X^3 − 2X^2 − 5X + 2
Y 2 = nDeriv(Y 1 ,X,X)
Y 3 = nDeriv(Y 2 ,X,X)
Graph Y 2 and find its zeros.
First use 0 as the left bound: When y = 0, x = 2.1196329.
Now use 0 as the right bound: When y = 0, x = −0.7862995.
Graph Y 3 and use TRACE to determine that the sign of the second derivative is negative at x =
−0.7862995, and positive at x = 2.1196329, and therefore the x-coordinate of the local
maximum will be −0.786.
Plug this value for x into the original equation or use TABLE to find the y-value for the local
maximum, which is about 4.209.
- A The Trapezoid Rule enables us to approximate the area under a curve with a fair degree of
accuracy. The rule says that the area between the x-axis and the curve y = f(x), on the interval
[a, b], with n trapezoids, is
[y 0 + 2y 1 + 2y 2 + 2y 3 + ... + 2yn−1 + yn]
Using the rule here, with n = 4, a = 0, and b = 1, we get
This is approximately 0.277.
- D First, make a quick sketch of the region.
