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Mathematics
Mathematics
Problem
Let us consider a curve,
y
=
f
(
x
)
y=f(x)
y
=
f
(
x
)
passing through the point
(
−
2
,
2
)
(-2,2)
(
−
2
,
2
)
and the slope of the tangent to the curve at any point
(
x
,
f
(
x
)
)
(x,f(x))
(
x
,
f
(
x
))
is given by
f
(
x
)
+
x
f
′
(
x
)
=
x
2
f(x)+xf'(x)=x^2
f
(
x
)
+
x
f
′
(
x
)
=
x
2
. Then a.
x
2
+
2
x
f
(
x
)
−
12
=
0
x^2 + 2xf(x) - 12 = 0
x
2
+
2
x
f
(
x
)
−
12
=
0
c.
x
3
−
3
x
f
(
x
)
−
4
=
0
x^3 - 3xf(x) - 4 = 0
x
3
−
3
x
f
(
x
)
−
4
=
0
b.
x
3
+
2
x
f
(
x
)
+
12
=
0
x^3 + 2xf(x) + 12 = 0
x
3
+
2
x
f
(
x
)
+
12
=
0
d.
x
2
+
2
x
f
(
x
)
+
4
=
0
x^2 + 2xf(x) + 4 = 0
x
2
+
2
x
f
(
x
)
+
4
=
0
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