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Question
Mathematics
Maximum slope of the curve y = -x3 + 3x2 + 9x - 27 is
Q. Maximum slope of the curve
y
=
−
x
3
+
3
x
2
+
9
x
−
27
is
1456
175
Application of Derivatives
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A
0
25%
B
12
38%
C
16
18%
D
32
18%
Solution:
y
=
−
x
3
+
3
x
2
+
9
x
−
27
Slope
=
d
x
d
y
=
m
=
−
3
x
2
+
6
x
+
9
Now,
d
x
d
m
=
−
6
x
+
6
Now,
d
x
d
m
=
0
⇒
−
6
x
+
6
=
0
⇒
x
=
1
Now,
d
x
2
d
2
m
=
−
6
<
0
∀
x
∴
x
=
1
is a point of local maximum.
∴
Maximum slope
=
−
3
(
1
)
2
+
6
(
1
)
+
9
=
12