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For the function g whose graph is given. Arrange the following numbers in increasing order and explain your reasoning. g(0), g'(-2), g'(0), g'(2), g'(4)

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Solution :
From the graph, the VALUE off(0) = 0.
Also TANGENT to` y = g(x) " at" x = 0` MAKES an obtuse ANGLE with thepositive x - AXIS, hence ` g'(0) lt 0`.
The measure of acute angle of inclination with the positive x - axis for tangent at ` x =- 2, x = 2, x = 4` is in decreasing order.
Hence ` g'(-2), gt g'(2) gt g'(4)`.
Thus, values in increasing order are ` g'(0) lt g(0) lt g'(4) lt g'(2) lt g'(-2)`.


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