How do you use the table below to find the slope of the tangent line at ? Choose the answer that best matches your slope.

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AP Calculus AB

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Define average and instantaneous rates of change at a point

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1 Sep 2020

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5. (18 pts) A curve is given by the equation tan-(y) + x + y In(x - 1) = 2. The questions (a) - (e) below are about this curve. (a) (10 pts) Find y, using implicit differentiation. Show your work. . (b) (2 pts) Verify that the point (2,0) lies on this curve. 1 2 3 4 5 6 ) (2 pts) A part of the curve that contains a point (2,0) is shown in the figure. In the figure above, draw the line tangent to the curve at the point (2,0). (d) (2 pts) Find the slope of the line tangent to the curve at the point (2,0). (e) (2pts) Write an equation of the line tangent to the curve at the point (2,0).

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Sr? - 4.0 +5 if x > 2 8. In all of this question let f(x) = { CPI-C if I <2 The letter c is a constant. (a) Find all values of c that makes the function f continuous at I = 2. Sufficiently justify your answer. [7 points) (b) On the same axis, make a sketch of the graphs of the function f for the values of c you found in Part (a). A tangent line to the curve y = f() has y-intercept of - 4. Find the equation of this tangent line. (10 points)

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