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X 3 (x-1) 2 ....find max. Or min. Value of x that is maxima and minima local

X3(x-1)2....find max. Or min. Value of x that is maxima and minima local
 

Grade:11

1 Answers

Arun
25763 Points
3 years ago
Dear student
 
f(x) = x³ (x-1)²
 
f'(x) = 3x² (x-1)² + 2(x-1)x³
 
f'(x) = 0
 
3x² (x-1)² + 2 (x-1)x³ = 0
 
x²( 3x² + 3 -6x + 2x² -2x) = 0
 
x = 0
 
And 
5x² -8x +3 = 0
(5x -3) (x-1) = 0
x = 3/5 and x = 1
 
Now
f" (x) = 
 
if f'' is negative then maxima will be obtained and if f" is positive then minima wilp be obtained

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