Answer:
Given curve is
y = 4x3
? 2x5 ? (1)
Let P(h, k) be a
point on (1)
K = 4h3
? 2h5 ?.(2)
(1)
m = slope of
tangent to (1)
= 12h2
? 10h4
Equation
of tangent to (1) at P(h, k) is
y ? K = m
(h ? h)
y ? K =
(12h2 ? 10h2) (x ? h) ?. (3)
(3) Passes
through (0, 0)
0 ? K =
(12h2 ? 10h4) (0 ? h)
K = 12h3
? 10h5 ?.. (4)
(2) and (3)
4h3
? 2h5 = 12h3 ? 10h5
8h5
? 8h3 = 0
h = 0,
?1, 1
(2) K = 0
when k = 0
K = ?4 + 2 = ? 2
when h
= ?1
K = 4 ? 2 = 2
when h = 1
Required points
are (0, 0), (?1, ?2) and (1, 2).
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