The function `f(x)=x(x+4)e^(-x//2)` has its local maxima at `x=adot` Then (a)`a=2sqrt(2)` (b) `a=1-sqrt(3)` (c)`a=-1+sqrt(3)` (d) `a=-4`

Discuss the global maxima and global minima of f(x)=tan^(-1)x-(log)_e x in [1/(sqrt(3)),sqrt(3)]

The values of parameter a for which the point of minimum of the function f(x)=1+a^2x-x^3 satisfies the inequality (x^2+x+2)/(x^2+5x+6)<0a r e (2sqrt(3),3sqrt(3)) (b) -3sqrt(3),-2sqrt(3)) (-2sqrt(3),3sqrt(3)) (d) (-2sqrt(2),2sqrt(3))

If tan^(-1)(a+x)/a+tan^(-1)(a-x)/a=pi/6,t h e nx^2= (a) 2sqrt(3)a (b) sqrt(3)a (c) 2sqrt(3)a^2 (d) none of these

f(x)=(x-1)|(x-2)(x-3)|dot Then f decreases in (a) (2-1/(sqrt(3)),2) (b) (2,2+1/(sqrt(3))) (c) (2+1/(sqrt(3)),4) (d) (3,oo)

Let f(x)=(alphax)/((x+1)),x!=-1. The for what value of alpha is f(f(x))=x (a) sqrt(2) (b) -sqrt(2) (c) 1 (d) -1

If two different tangents of y^2=4x are the normals to x^2=4b y , then (a) |b|>1/(2sqrt(2)) (b) |b| 1/(sqrt(2)) (d) |b|<1/(sqrt(2))

(1)/(sqrt(x+3)-sqrt(x-4))

int_(-1)^(1/2)(e^x(2-x^2)dx)/((1-x)sqrt(1-x^2))i se q u a lto (sqrt(e))/2(sqrt(3)+1) (b) (sqrt(3e))/2 sqrt(3e) (d) sqrt(e/3)

If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(1-x^2))=pi/3, w h e r e|x|<1, then x is equal to (a) 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) sqrt(3) (d) -(sqrt(3))/4

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)