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Calculus: Differentiation and Integration, 1st Edition
book

Calculus: Differentiation and Integration, 1st Edition

by ICFAI
April 2024
Intermediate to advanced content levelIntermediate to advanced
710 pages
20h 50m
English
Pearson India
Content preview from Calculus: Differentiation and Integration, 1st Edition
7-16  Calculus – Differentiation and Integration
Then the distance between (x, y) and (3, 0) is given by
S x y x x y
x x x
x x
= + = + +
= + +
= +
( ) ( )
.
3 0 9 6
9 6 5
7 14
2 2 2 2
2
2
Now, we need to minimise the distance S.
We have
dS
dx
x
x x
=
+
2 7
2 7 14
2
.
Thus,
dS
dx
x x
x
x
=
+
=
=
0
1
2 7 14
2 7 0
7
2
2
( )
.
Thus,
y =
3
2
. And clearly, S is minimum at x = 7/2.
Therefore, the nearest point to the point (3, 0) on the graph of
5- x is
7
2
3
2
, .
And the shortest possible distance is
S =
7
2
.
Example 7.12 Find the equations of the tangent lines with maximum and minimum slopes of all the
tangent lines to the curve
y
x
=
+
3
3
2
.
Solution: The slope of ...
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Publisher Resources

ISBN: 9789353948221