Use the asymptotic behaviour of f = sin(πx) + xe^−x to sketch its graph. Include the graphs of y = xe^−x and y = sin(πx) and discuss the behaviour of the graph of f relative to these two graphs.

Find all x-values on the graph of f(x) = −3sin(x)cos(x) where the tangent line is horizontal. Be sure that your answer communicates in mathematical notation ALL the values where this is the case, and use a graph to support your answer.

do not copy

Sketch the graphs of f(x) = arccos (cos(x)) and g(x)= cos(arccos(x)) on the separateaxes below. Explain, in terms of the meaning of the input and output quantities of thesefunctions, why your graphs look as they do. Your graphs should clearly indicate the domainand range of the functions f and g.

please help with Part B

7) Find the derivatives using the rules of differentiation. Express results with positive exponents. a) f(x) = -2x5 - 3x³ + x b) g(x) = −6³√√x + 2√√x -4- c) f(0) = 2 sec 0 tane - 80