Provided function f(x)=x^3 - 2x + 1. Let c1=-1, c2=0. a. Calculate f(c1).
Find slopes of the secant lines connecting (x,f(x)) and (c1,f(c1)), using the list of x-values: [-1.5, -1.3, -1.1, -0.9, -0.7, -0.5].
b. Compute f(c2). Find slopes of the secant lines connecting (x,f(x)) and (c2,f(c2)), using list of x-values: [-0.5, -0.3, -0.1, 0.1, 0.3, 0.5].
c. Find slope of tangent at c1, and similarly at c2. Explain your observations.
d. Graph function, along with line equations of evaluated tangents through points (c1,f(c1)) and (c2,f(c2)). 2. Given function f(x)=x^3 - 2x + 4. Let [-1.5, 1.5] define interval.
a. Partition interval into 6 sub-intervals. Let u1,u2,...,u6 be centers of sub-intervals. Calculate f(u1),...,f(u6), and use these values to find out area under the curve.
b. Partition interval into 3 sub-intervals. Repeat process, as in part a.
c. Graph function (but not all rectangles). Compare results of parts a and b.