Math 124 Name _______________#10 THE DERIVATIVE FUNCTION 2.31. Consider the function graphed below.(a) On this graph, sketch the graph of the derivative function )(xfy.(b) The function f is increasing on the interval(s) _________________________.The slopes of the tangent lines to f are positive on the interval(s) _________________.If 0)( xf on an interval, then f is ________________________ over that interval.REMEMBER THAT THE SLOPE OF THE TANGENT LINE TO f AT a IS THE SAME AS )(af.(c) The function f is decreasing on the interval(s) _________________________.The slopes of the tangent lines to f are negative on the interval(s) ________________.If 0)( xf on an interval, then f is ________________________ over that interval.1Math 124 Name _______________2. Sketch the graph of the derivative function for each of these.(a) (b) (c)2Math 124 Name _______________3. Sketch the graph of the derivative of each of the following functions.3 -3-2-10123-6 -4 -2 0 2 4 6 -3-2-10123-6 -4 -2 0 2 4 6 -3-2-10123-6 -4 -2 0 2 4 6 -3-2-101234-6 -4 -2 0 2 4 6 -3-2-10123-6 -4 -2 0 2 4 6 -1-0.75-0.5-0.2500.250.50.751-3 -2 -1 0 1 2 3
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