Home
Class 12
MATHS
If f(x)=x e^(x(x-1)) , then f(x) is incr...

If `f(x)=x e^(x(x-1))` , then `f(x)` is increasing on `[-1/2,1]` decreasing on `R` increasing on `R` (d) `` decreasing on `[-1/2,1]`

A

increasing in `[-1//2, 1]`

B

decreasing in R

C

increasing in R

D

decreasing in `[-1//2, 1]`

Text Solution

Verified by Experts

The correct Answer is:
B
Given, ` f(x) = x e ^(x ( 1 - x))`
`rArr f ' (x) = e ^(x(1- x)) + x e (x (1- x)) (1 - 2x ) `
`" " = e ^(x(1- x)) [ 1 + x (1 - 2x )]`
`" " = e ^(x ( 1 - x )) ( 1+ x - 2x ^(2))`
`" " = - e^(x (1 - x )) ( 2x^(2) - x - 1)`
` " " = - e^(x( 1-x )) (x -1) (2 x + 1)`
Which is positive in `(-(1)/(2), 1)`
Therefore, `f(x)` is increasing in `[- (1)/(2), 1]`
Promotional Banner

Similar Questions

Explore conceptually related problems

If f(x)=xe^(x(x-1)), then f(x) is (a) increasing on [-(1)/(2),1] (b) decreasing on R (c) increasing on R(d) decreasing on [-(1)/(2),1]

the function f(x)=x^2-x+1 is increasing and decreasing

Let f(x): [0, 2] to R be a twice differenctiable function such that f''(x) gt 0 , for all x in (0, 2) . If phi (x) = f(x) + f(2-x) , then phi is (A) increasing on (0, 1) and decreasing on (1, 2) (B) decreasing on (0, 2) (C) decreasing on (0, 1) and increasing on (1, 2) (D) increasing on (0, 2)

f:R rarr R,f(x) is differentiable such that f(f(x))=k(x^(5)+x),k!=0). Then f(x) is always increasing (b) decreasing either increasing or decreasing non-monotonic

Let f(x)=tan^(-1)(g(x)) , where g(x) is monotonically increasing for 0

Show that f(x)=(1)/(1+x^(2)) is neither increasing nor decreasing on R.

f(x) = (1-x)^(2) cdot sin^(2) x + x^(2) ge 0, AA x and g(x) =int_(1)^(x) ((2(t-1))/((x+1))-log t ) f (t) dt Which of the following is true? (A)g is increasing on (1,infty) (B)g is decreasing on (1, infty) (C) g is increasing on (1,2) and decreasing on (2, infty) (D) g is decreasing on (1,2) and increasing on (2,infty)

The function defined by f(x)=(x+2)e^(-x) is (a)decreasing for all x (b)decreasing in (-oo,-1) and increasing in (-1,oo) (c)increasing for all x (d)decreasing in (-1,oo) and increasing in (-oo,-1)

f(x)=int(2-(1)/(1+x^(2))-(1)/(sqrt(1+x^(2))))dx then fis (A) increasing in (0,pi) and decreasing in (-oo,0)(B) increasing in (-oo,0) and decreasing in (0,oo)(C) increasing in (-oo,oo) and (D) decreasing in (-oo,oo)

If f(x)=2x+cot^(-1)x+log(sqrt(1+x^(2))-x) then f(x)( a)increase in (0,oo)( b)decrease in [0,oo]( c)neither increases nor decreases in [0,oo]( d) increase in (-oo,oo)