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The function $f(x)=x^{5}-5x^{4}+5x^{3}-1$ has

1. one minima and two maxima
2. two minima and one maxima
3. two minima and two maxima
4. one minima and one maxima

one maximum  and one minimum points are found by diffrerentiating and finding the maxima and minima points.

upon double diffrerentiating and putting these value ,one maximum  where double differentiating value found positive and one minimum where double diffrentiaion value is negative.

option A will be correct.

as above soluition\

for x = 0, f''(0) =0

and for x=1  f''(1) = -10  (maxima)

for x= 3  f''(3) =  -20 (maxima)

why option D ??
thanks for reminding me.
This is incorrect.

We are supposed to put x=3 in f’’(x). Instead he has put x=2.

f’’(3) = 90 which is a minima

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