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Mathematics
Mathematics
Problem
At what points of curve
y
=
2
3
x
3
+
1
2
x
2
y = \frac{2}{3}x^3 + \frac{1}{2}x^2
y
=
3
2
x
3
+
2
1
x
2
, tangent makes the equal angle with axis (a)
(
1
2
,
5
24
)
\left(\frac{1}{2}, \frac{5}{24}\right)
(
2
1
,
24
5
)
and
(
−
1
,
−
1
6
)
\left(-1, -\frac{1}{6}\right)
(
−
1
,
−
6
1
)
(b)
(
1
2
,
4
9
)
\left(\frac{1}{2}, \frac{4}{9}\right)
(
2
1
,
9
4
)
and
(
−
1
,
0
)
(-1, 0)
(
−
1
,
0
)
(c)
(
1
3
,
1
7
)
\left(\frac{1}{3}, \frac{1}{7}\right)
(
3
1
,
7
1
)
and
(
−
3
,
1
2
)
\left(-3, \frac{1}{2}\right)
(
−
3
,
2
1
)
(d)
(
1
3
,
4
47
)
\left(\frac{1}{3}, \frac{4}{47}\right)
(
3
1
,
47
4
)
and
(
−
1
,
−
1
3
)
\left(-1, -\frac{1}{3}\right)
(
−
1
,
−
3
1
)
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