Consider the function f(x) = sin( /24 )x + cos(x) on the domain [0, 4]. (i) Find
ID: 2862542 • Letter: C
Question
Consider the function f(x) = sin( /24 )x + cos(x) on the domain [0, 4].
(i) Find the critical points of f and determine the intervals on which f is increasing and the intervals on which it is decreasing.
(ii) Which of the critical points are local maxima and which are local minima?
(iii) Check that the second-derivative test gives the same answer as found in (ii).
(iv) Evaluate f at each of its critical points and at the endpoints of the interval and thus find the global maximum and minimum values of f on the interval [0, 4].
(v) From your calculations in (iv), determine how many solutions the equation
sin( /24 )x + cos(x) = 0 () has in the interval [0, 4].
Explanation / Answer
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