(a) Find maximum and minimum value of y = (x - 2)^6 (x - 3)^5
Answers
Answer:
y=(x−2)
6
(x−3)
5
.
Differentiating, we get
dx
dy
=6(x−2)
5
(x−3)
5
+5(x−3)
4
(x−2)
6
=(x−2)
5
(x−3)
4
(11x−28)
∴
dx
dy
=(x−2)
4
(x−3)
4
.11(x−2)(x−
11
28
)
For maxima or minima,
dx
dy
=0
⇒x=2,3,
11
28
Now at x=2,
dx
dy
changes from +ive to -ive.
∴ Maximum is at x=2 and maximum value is 0.
At x=
11
28
,
dx
dy
changes from -ive to +ive ∴ minimum at x=
11
28
∴ Minimum value of y=(
11
28
−2)
6
(
11
28
−3)
5
=(
11
6
)
6
(
11
−5
)
5
=−
11
11
5
5
6
6
At x=3,
dx
dy
changes from +ive to +ive ∴ Neither minimum nor maximum at x=3.
this is answer
Answer:
X max=2,x min=3
Step-by-step explanation:
Correct option is
C
x
max
=2,x
min
=3
Given y=(x−2)
6
(x−3)
5
.
Differentiating, we get
dx
dy
=6(x−2)
5
(x−3)
5
+5(x−3)
4
(x−2)
6
=(x−2)
5
(x−3)
4
(11x−28)
∴
dx
dy
=(x−2)
4
(x−3)
4
.11(x−2)(x−
11
28
)
For maxima or minima,
dx
dy
=0
⇒x=2,3,
11
28
Now at x=2,
dx
dy
changes from +ive to -ive.
∴ Maximum is at x=2 and maximum value is 0.
At x=
11
28
,
dx
dy
changes from -ive to +ive ∴ minimum at x=
11
28
∴ Minimum value of y=(
11
28
−2)
6
(
11
28
−3)
5
=(
11
6
)
6
(
11
−5
)
5
=−
11
11
5
5
6
6
At x=3,
dx
dy
changes from +ive to +ive ∴ Neither minimum nor maximum at x=3.
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