The graph of a function f is given to the below. Use it to sketch the graph of the derivative f'. y = f(x) 1- SOLUTION We can estimate the value of the derivative at any value of x by drawing the tangent at the point (x, f(x)) and estimating its slope. For instance, for x = 3 we draw a tangent at P in the figqure below and estimate its slope to be about – (We have drawn a triangle to help estimate the slope.) Thus f'(3), rounded to two decimal places, is approximately .6 and this allows us to plot the point, with coordinates rounded to two decimal places, P( on the graph f' directly beneath P. (The slope of the graph of f becomes the y-value on the graph of f'.)

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