Question

Find an if the function f(x) = x-x³ in -π

Answer 1

Step-by-step explanation:

Correct option is A)

f(x)=x

3

−9kx

2

+27x+30 is increasing on R.

f(x)=x

3

−9kx

2

+27x+30

f

′

(x)=3x

2

−18kx+27

=3(x

2

−6kx+9)

Given f(x) is increasing on R

⇒f

′

(x)>0 for all x∈R

⇒3(x

2

−6kx+9)>0

(x

2

−6kx+9)>0 all x∈R

ax

2

+bx+c>0

so, (−6k)

2

−4(1)(9)<0

⇒36k

2

−36<0

(k+1)(k−1)<0

It can be possible when (k+1)<0 and d(k−1)>0

⇒k<−1 and k>1 (not possible)

or, (k+1)>0 and (k−1)<0

k>−1 and k<1

−1<k<1 so option A is correct.