determine the maximum and minimum value of2x^3-9x^2y+12xy^2-60y.
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Class 12
>>Maths
>>Application of Derivatives
>>Maxima and Minima
>>The minimum value of 2x^3 - 9x^2 + 12x +
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The minimum value of 2x
3
−9x
2
+12x+4 is
Medium
Solution
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Correct option is E)
Let y=2x
3
−9x
2
+12x+4
On differentiating w.r.t x we get
dx
dy
=6x
2
−18x+12
f
′
(x)=0
∴6x
2
−18x+12=0
⇒x
2
−3x+2=0
⇒x=2or1
Now,
dx
2
d
2
y
=12x−18>0
or x=2
∴ x=2 is a point of local minima and y
min
=16−36+24+4=8
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