Given the graph of f(x) below, complete the chart, estimating the derivate (slop

Question

Given the graph of f(x) below, complete the chart, estimating the derivate (slope of the tangent line) at the given values of x. It is sometimes helpful to use your pencil as a tangent line. After completing the chart, graph the ordered pairs in the chart. Connecting the points with a smooth curve will graph the derivative of f(x). What do you notice about the y-value of the graph of the derivative when the function reaches a relative maximum? What do you notice about the y-value of the graph of the derivative when the function reaches a relative minimum? What do you notice about the y-values of the graph of the derivative when the function is Increasing? What do you notice about the y-values of the graph of the derivative when the function is decreasing?

Explanation / Answer

a) At relative maximuma derivative become 0, so y value will be 0. And it's change sign from positive to negative.

b) At relative minima derivative become 0, so y value will be 0. And it's change sign from negitive to positive.

c) Derivative is positive for increasing function.

d) Derivative is negative for decreasing function.

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