04 - Normal Lines - Kuta Software

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Kuta Software - Infinite Calculus
Normal Lines
Name___________________________________
Date________________
Period____
For each problem, find the equation of the line normal to the function at the given point. If the normal line
is a vertical line, indicate so. Otherwise, your answer should be in slope-intecept form.
1) y = x 3 − x 2 − 2 at (1, −2)
8
6
4
2
y
−6 −4 −2 2 4 6 8
−2
−4
−6
−8
x
2) y =
1
x − 4
8
6
4
2
y
at (5, 1)
x
−2 2 4 6 8 10 12
−2
−4
−6
3) y = −x 3 + 15x 2 − 72x + 110 at (4, −2)
4) y =
2
x − 3
at (5, 1)
5) y =
3
x + 2 at ( 4, 1 2) 6) y = (2x − 8)
1
3 at (0, −2)
7) y = ln (x + 4) at (−3, 0)
8) y = −sin (2x) at
( − π 2 , 0 )

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Kuta Software - Infinite Calculus
Name___________________________________
Normal Lines
Date________________
Period____
For each problem, find the equation of the line normal to the function at the given point. If the normal line
is a vertical line, indicate so. Otherwise, your answer should be in slope-intecept form.
1) y = x 3 − x 2 − 2 at (1, −2)
y
8
6
4
2
2) y =
1
x − 4
y
8
6
4
at (5, 1)
x
−6 −4 −2 2 4 6 8
−2
x
2
−4
−6
−8
−2 2 4 6 8 10 12
−2
−4
−6
y = −x − 1
y = x − 4
3) y = −x 3 + 15x 2 − 72x + 110 at (4, −2)
Normal line is vertical line at x = 4
2
4) y = at (5, 1)
x − 3
y = 2x − 9
5) y =
3
x + 2 ( at 4, 1 2)
y = 12x − 95
2
1
6) y = (2x − 8)
3 at (0, −2)
y = −6x − 2
7) y = ln (x + 4) at (−3, 0)
y = −x − 3
8) y = −sin (2x) at
( − π 2 , 0 )
y = − 1 2 x − π 4
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