Consider the function fx shown in the graph below Use the gr

Consider the function f(x) shown in the graph below Use the graph above to estimate the derivative of f at the points shown in the table below. At a given point place a straightedge so that it forms the line tangent to the graph of f at that point, and then use the grid to estimate the slope of the tangent line You can double check those values by carefully sketching the graph of derivative function, f\'.

Solution

Draw Tangent at x = -3.Tangent pases through (-3, -1) and (-4 ,-3)

slope = (-3+1)/(-4 +3) = 2 = f\'(x)

Draw a tangent at x =-1.Tangent parallel to x axis

slope = 0 = f\'(x)

Draw a tangent at x = 1.Tangent passes through ( 1 , -1.5) and (0, 3)

slope = (3 +1.5)/(0 -1) = -4.5 = f\'(x)

Draw a tangent at x =3 .Tangent passes through ( 3 , -6) and (2 , -7)

slope = ( -7 +6)/(2 -3) = -1/-1 = 1 = f\'(x)