Find the interpolating polynomial of the following point and function using Lagrange interpolation process. 1. (-3,0), (-1,2), (0,-2), (1,3) and (3,-1). 2. y = cos ( 2x ) at x = [0,π] with four equally spaced points.

4. Consider the functions k(x) = 27" and m(x) = 9 · 3". (a) Are k(x) and m(x) the same function? Explain. (b) Write m(x) as a composition of f(x) = 3ª and another function b(x), so that m(x) = b(f(x)). Give the function b(x). = 3" and another function d(x), so that k(x) = d(f(x)). Give (c) Write k(x) as a composition of f(x) the function k(x).

Consider the following. Function f(x)=√x-4 Point (5, 1) (1,5) =x²+4, X20 Find the slope of the graph of f at the point (5, 1). Find the slope of the graph of f1 at the point (1, 5). Are the slopes of the graphs of f at the point (5, 1) and f-1 at the point (1, 5) reciprocals of one another? O Yes, the slopes are reciprocals of one another. O No, the slopes are not reciprocals of one another. Need Help? Read It

Suppose (x)= -4x. Determine and graph four distinct antiderivatives of f. Refer to image below of graph