Math 220 March 7 I. If 1200 cm2 of material is available to make a ...

D = (x − 4) 2 + (y − 0) 2
D(x) = (x − 4) 2 + ( √ x) 2
D(x) = √ x 2 − 8x + 16 + x
D(x) = √ x 2 − 7x + 16
D ′ 2x − 7
(x) =
2 √ x2 − 7x + 16
2x − 7
0 =
2 √ x2 − 7x + 16
0 = 2x − 7
x = 7
2
D ′ (x) < 0 when x < 7/2
D ′ (x) > 0 when x > 7/2
Thus there is a minimum at x = 7/2
The point (7/2, 7/2) is closest.
III. At which points on the curve y = 1 + x + 60x 3 − x 5 does the tangent
line have the largest slope?
Answer:
slope = y ′ = 180x 2 − 5x 4
4