# FIND EQUATION OF THE TANGENT LINE AT A GIVEN POINT WORKSHEET

For each problem, find the equation of the tangent line to the function at the given point.

Problem 1 :

f(x) = x2 + 1; (1, 2)

 A)  y = 2xC)  y = (1/2)x + 3/2 B)  y = -8x + 10D)  y = -6x + 8

Solution

Problem 2 :

f(x) = 2x2 + 2x + 2; (-1, 2)

 A)  y = -8x – 6C)  y= (1/2)x + 5/2 B)  y = -2xD)  y = 6x + 8

Solution

Problem 3 :

y = x2 + x - 2; (1, 0)

 A) y = 34x - 34             C) y = 3x - 3 B) y = -32x + 32        D)  y = -12x + 12

Solution

Problem 4 :

y = 2x2 + 1; (-1, 3)

A)  y = 2x + 5        B)  y = -4x – 1     C)  y = 12x + 15

Solution

Problem 5 :

 A) y = (1/4)x + 1C) y = -x + 1 B)  -2x + 1D)  y = 1

Solution

Problem 6 :

 A ) y = - 34x + 1 C) y = 34x - 2 B) y = 14x - 1 D) y = x - 52

Solution

Problem 7 :

 A)  y = -1 C)  y = -(1/2)x - 2 B)  y = x + 1D)  y = 4x + 7

Solution

Problem 8 :

Solution

1)  y = 2x, option (A)

2)  y = -2x, option B

3)  y = 3x - 3, option C

4)  y = -4x - 1, option B

5)  y = -x + 1, option C

6)  y = (1/4)x - 1, option C

7)  y = x + 1, option B

8)  y = -(1/4) x - (3/4)

For each problem, find the equation of the line tangent to the function at the given point. Your answer should be in slope – intercept form.

Problem 1 :

y = x3 – 3x2 + 2 at (3, 2)

Solution

Problem 2 :

Solution

Problem 3 :

y = x3 – 2x2 + 2 at (2, 2)

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Solution

Problem 7 :

y = In (-x) at (-2, In 2)

Solution

Problem 8 :

y = -2tan (x) at (-π, 0)

Solution

1)  y = 9x - 25

2)  y = (-5/2)x -5

3) y = 4x - 6

4)  y = -8x/27 - (23/27)

5)  y = (2/3)x + 1/3

6)  y = (1/2)x + 3

7)  y = (-1/2)x + ln 2 - 1

8)  y = -2x - 2π

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