04 - Normal Lines - Kuta Software
04 - Normal Lines - Kuta Software
04 - Normal Lines - Kuta Software
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
©O c2U0p1c3m kKruot8aN hSEovfWtlw7awrKeJ iLxLRC2.Z x 4Afl1lU ArciGgWhvtqsC WreeSsgeIrYvze6dK.i i yMraMdveH owhistMh5 cIjnPfpi3nCiNtTe5 bCKa8lAcyudlRuesj.X Worksheet by <strong>Kuta</strong> <strong>Software</strong> LLC<br />
<strong>Kuta</strong> <strong>Software</strong> - Infinite Calculus<br />
<strong>Normal</strong> <strong>Lines</strong><br />
Name___________________________________<br />
Date________________<br />
Period____<br />
For each problem, find the equation of the line normal to the function at the given point. If the normal line<br />
is a vertical line, indicate so. Otherwise, your answer should be in slope-intecept form.<br />
1) y = x 3 − x 2 − 2 at (1, −2)<br />
8<br />
6<br />
4<br />
2<br />
y<br />
−6 −4 −2 2 4 6 8<br />
−2<br />
−4<br />
−6<br />
−8<br />
x<br />
2) y =<br />
1<br />
x − 4<br />
8<br />
6<br />
4<br />
2<br />
y<br />
at (5, 1)<br />
x<br />
−2 2 4 6 8 10 12<br />
−2<br />
−4<br />
−6<br />
3) y = −x 3 + 15x 2 − 72x + 110 at (4, −2)<br />
4) y =<br />
2<br />
x − 3<br />
at (5, 1)<br />
5) y =<br />
3<br />
x + 2 at ( 4, 1 2) 6) y = (2x − 8)<br />
1<br />
3 at (0, −2)<br />
7) y = ln (x + 4) at (−3, 0)<br />
8) y = −sin (2x) at<br />
( − π 2 , 0 )
©H U2z0F1h31 ZKHu9t2aw jSiomftttw1aYrlex ALbLgCp.v l HABl2lL 5rHidgvhGt2sz UrPeZsxearCvQepd0.7 o VMUajdAe4 Iwpi4tmhF rIEnffIi6nOiQtre5 ZCSaVlQcLu0lZu8s0.b Worksheet by <strong>Kuta</strong> <strong>Software</strong> LLC<br />
<strong>Kuta</strong> <strong>Software</strong> - Infinite Calculus<br />
Name___________________________________<br />
<strong>Normal</strong> <strong>Lines</strong><br />
Date________________<br />
Period____<br />
For each problem, find the equation of the line normal to the function at the given point. If the normal line<br />
is a vertical line, indicate so. Otherwise, your answer should be in slope-intecept form.<br />
1) y = x 3 − x 2 − 2 at (1, −2)<br />
y<br />
8<br />
6<br />
4<br />
2<br />
2) y =<br />
1<br />
x − 4<br />
y<br />
8<br />
6<br />
4<br />
at (5, 1)<br />
x<br />
−6 −4 −2 2 4 6 8<br />
−2<br />
x<br />
2<br />
−4<br />
−6<br />
−8<br />
−2 2 4 6 8 10 12<br />
−2<br />
−4<br />
−6<br />
y = −x − 1<br />
y = x − 4<br />
3) y = −x 3 + 15x 2 − 72x + 110 at (4, −2)<br />
<strong>Normal</strong> line is vertical line at x = 4<br />
2<br />
4) y = at (5, 1)<br />
x − 3<br />
y = 2x − 9<br />
5) y =<br />
3<br />
x + 2 ( at 4, 1 2)<br />
y = 12x − 95<br />
2<br />
1<br />
6) y = (2x − 8)<br />
3 at (0, −2)<br />
y = −6x − 2<br />
7) y = ln (x + 4) at (−3, 0)<br />
y = −x − 3<br />
8) y = −sin (2x) at<br />
( − π 2 , 0 )<br />
y = − 1 2 x − π 4<br />
Create your own worksheets like this one with Infinite Calculus. Free trial available at <strong>Kuta</strong><strong>Software</strong>.com