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)`

Explanation

From the graph, the value of f(0) = 0.
Also tangent to ` y = g(x) " at" x = 0` makes an obtuse angle with the positive 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)`.