Page 213 - How To Solve Word Problems In Calculus

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6. Let f (x) = x . The slope of the tangent line at (2, 4) is m = f (2).
f (x) = x 2

f (x) = 2x
f (2) = 4

The equation of the tangent line can be constructed using the
standard equation for a line:

y − y 1 = m(x − x 1 )
y − 4 = 4(x − 2)

y − 4 = 4x − 8

y = 4x − 4
Once we sketch the curve and the tangent line, it becomes clear
that horizontal rectangles are best to use.

6 6

4 4 (2,4)

2 2
(x,y)
1 (x,y)
2
1 1 2 2

− 2
−2
√
2
Solving for x in terms of y, the equation y = x becomes x = y
y + 4
and y = 4x − 4 becomes x = .
4
4
A = (x 2 − x 1 ) dy
0

4

y + 4 √
= − y dy
0 4
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