Question

EX #5: Based on the definition above, identify the following: A. Relative Maximum is __ where x = __ B. Relative Minimum is __ where x = __ C. Relative Minimum is __ where x = __

Answer 1

Based on the given graph, you can conclude:

A. Relative Maximum is f(x) = 1 where x = 2

(Because the relative maximum of a function is given by a point of the graph with a slope m = 0, but this point is not necessarily the absolute maximum. Furthermore, the concavity of the curve at this point is negative).

B. Relative minimum is f(x) = -8 where x = -3

C. Relative minimum is f(x) = 0 where x = 4

Both relative minima correspond to points in which the slope of the line is 0 and the concavity of the line is positive.