Question

4x3 + 6x² - x by - 1/2x​

Answer 1

Given : f(x)=x

4

−4x

3

+6x

2

−4x+1

Differentiate w.r.t x

f

′

(x)=4x

3

−12x

2

+12x−4

=4(x

3

−3x

2

+3x−1)

=4(x−1)

3

i)ifx

′

≥1,f

′

(x)≥0 (Therefore option A is correct)

ii) equate f

′

(x)=0

4(x−1)

3

=0

x=1

iii) f

′′

(x)=12(x−1)

2

f

′′

(x)=0[ifx=1]

f

′′

(x)

f

′′′

(x)=24(x−1)[if(x=1)]

f

′′′′

(x)=+24>0

Therefor this becomes point of minima at x=0⇒ option C is zero.

I give two example please solve you by yourself