February 8, 2018
###### Compare/Contrast · Treaties vs. Executive Agreements
February 9, 2018

NEED THIS DONE IN MAPLE SOFT! 1. Given the function f(x)=x3â 2x+1fxx32x1. Let c1=-1, c2=0. a. Calculate f(c1). Determine the slopes of a…

1. Given the function f(x)=x3-2x+1fxx32x1. Let c1=-1, c2=0.

a. Calculate f(c1). Determine the slopes of a secant lines connecting (x,f(x)) and (c1,f(c1)),

using this list of x-values: [-1.5, -1.3, -1.1, -0.9, -0.7, -0.5].

b. Calculate f(c2). Determine the slopes of a secant lines connecting (x,f(x)) and (c2,f(c2)),

using this list of x-values: [-0.5, -0.3, -0.1, 0.1, 0.3, 0.5].

c. Estimate the slope of the tangent at c1, and similarly at c2. Describe your observations.

d. Graph the function, along with the line equations of the estimated tangents through points (c1,f(c1)) and (c2,f(c2)).

2. Given the function f(x)=x3-2x+4fxx32x4. Let [-1.5, 1.5] define an interval.

a. Partition the interval into 6 sub-intervals. Let u1,u2,…,u6 be the centers of the sub-intervals.

Compute f(u1),…,f(u6), and use these values to determine the area under the curve.

b. Partition the interval into 3 sub-intervals. Repeat the process, as in part a.

c. Graph the function (but not all the rectangles). Compare the results of parts a and b.