Q30.Solve the equation (x-5)/3 = (x-
3)/5
sk
O
X = 10
O O
X=16
O
X=8
O X=12
Answers
the ans is 12 because you need to substitute for some reason
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12th
Maths
Application of Derivatives
Maxima and Minima
The function x5 - 5x4 + 5x3...
MATHS
The function x
5
−5x
4
+5x
3
−10 has a maximum, when x=
EASY
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ANSWER
To obtain the absolute maxima or minima for the function f(x)
Find f
′
(x) and put f
′
(x)=0
Given
x
5
−5x
4
+5x
3
−10
f(x)=x
5
−5x
4
+5x
3
−10
f(x)=x
5
−5x
4
+5x
3
−10
dx
df(x)
=f
′
(x)=5x
4
−20x
3
+15x
2
5x
4
−20x
3
+15x
2
=0
5x
2
(x−3)(x−1)=0
x=0, x=1, x=3
To find the maximum find f
′′
(x) and substitute the value of x
dx
df
′
(x)
=f
′′
(x)=20x
3
−60x
2
+30x
When, x=3
f
′′
(x)=20x
3
−60x
2
+30x=20(3)
3
−60(3)
2
+30(3)=90 >0
When, x=0
f
′′
(x)=20x
3
−60x
2
+30x=20(0)
3
−60(0)
2
+30(0)=0
When, x=1
f
′′
(x)=20x
3
−60x
2
+30x=20(1)
3
−60(1)
2
+30(1)=−10 <0
∴ The given function has the maximum value when x=3