AP Exam Review

Tangent Lines

4) The equation of the tangent line to the curve at the point (1, 7) is

(a) (b) (c)

(d) (e)

7) If the line is tangent to the curve , then c is

(a) 2 (b) 4 (c) 7 (d) 11 (e) 15

32) At what point on the curve is the tangent line vertical?

(a) (0, 0) only (b) (-1, 0) only (c) only

(d) (-1, 0) and (0, 0) (e) The tangent line is never vertical.

39) Let f and g be functions that are differentiable for all real numbers x with . If is an equation of the line tangent to the graph of f at , what is the equation of the line tangent to the graph of y at ?

(a) (b) (c) (d) (e)

43) Let f be the function given by . The tangent line to the graph at is used to approximate . What is the error in this approximation?

(a) 0 (b) 0.008 (c) 0.248 (d) 0.400 (e) 0.648

45) Find the y-intercept of the line tangent to at .

(a) -21.032 (b) -2.081 (c) 0 (d) 4.161 (e) 21.746

23) The curve passes through (3, 0). Use local linearization to estimate the value of y at . The value is

(a) -2.7 (b) -0.9 (c) 0 (d) 0.1 (e) 3.0

10) An equation of the line tangent to at is

(a) (b)

(c) (d)

(e)

17) Find the equation of the tangent line to through (2, -1).

(a) (b) (c) (d)

(e)

8) An equation of the line normal to at (2, 4) is

(a) (b) (c)

(d) (e)

13) The slope of the line tangent to the graph of at (2, 1) is

(a) (b) (c) (d) 12 (e) -7

22) Find the slope of the normal line to at (0, 1).

(a) 1 (b) -1 (c) 0 (d) 2 (e) undefined

40) Which of the following is an equation of the line tangent to the graph of at ?

(a) (b) (c) (d)

(e)

12) What is the equation of the line tangent to the graph of at ?

(a) (b) (c)

(d) (e)

29) If is the function given by , at what value of x is the slope of the tangent line to equal to 2?

(a) -0.135 (b) 0 (c) 0.231 (d) -0.366 (e) 0.693

32) Let f be the function given by . For what value of x is the slope of the line tangent to the curve at equal to 1?

(a) 1.099 (b) 0.086 (c) 0 (d) -0.086 (e) -1.099

6) The tangent line to the curve at the point (2, 8) has an x-intercept at

(a) (-1, 0) (b) (1, 0) (c) (0, -8) (d) (0, 8) (e) (8, 0)

15) The equation of the line normal to at is

(a) (b) (c)

(d) (e)

1) What is the slope of the line tangent to the curve when ?

(a) (b) (c) -1 (d) 0 (e)

7) The line normal to the curve at has slope

(a) (b) (c) 1 (d) (e) -1