Question

If $F\left(x\right)=2x^3-21x^2+36x-20$, then

• A. f has maxima at x=1
• B. f has minima at x=1
• C. f has maximum value -128
• D. f has minimum value -3

Answer 1

Answer: (A)

f has maxima at x=1

Consider given the function,

$F\left(x\right)=2x^3-21x^2+36x-20$ ……(1)

Differentiate with respect to x,

$F^{{}^{\prime }}\left(x\right)=6x^2-42x+36$ ……..(2)

For maxima and minima,

$F\left(x\right)=0$

$6x^2-42x+36=0$

$x^2-7x+6=0$

$x^2-6x-x+6=0$

$x(x-6)-1(x-6)=0$

$(x-6)(x-1)=0$

$x=1,6$

Differentiate equation 2^nd with respect to x,

$F^{{}^{\prime \prime }}\left(x\right)=12x-42$

At $x=1\Rightarrow F^{{}^{\prime \prime }}\left(x\right)<0$

Hence, F(x) Is maximum.

At $x=6\Rightarrow F\left(x\right)>0$

Hence, function F(x) is minimum.

Hence, this is the answer.