Answer:
Let
P(h, k) be the required point.
lies on
given curve
y
= x3 ? 3x2 ? 9x + 7 ?. (1)
K = h3
? 3h2 ? 9h + 7 ?. (2)
Diff.
(1) w.r.t. x
m
= slope of tangent to (1)
Now
the tangent to (1) is || to X-axis if m =0
3h2
? 6h ? 9 = 0
h2 ?
2h ? 3 = 0
h2
? 2h + h ? 3 = 0
h (h ? 3)
+ (h ? 3) = 0
(h ? 3) (h
+ 1) = 0
h = 3, ?1
when
h = 3, (2)
K = 27 ?
27 ? 27 + 7 = ?20
when
h = ?1, (2)
K = ?1 ? 3
+ 9 + 7 = 12
Required
points are (3, ?20), (?1, 12).
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