The maximum value of the function `f(x)=((1+x)^(0. 6))/(1+x^(0. 6))` in the interval `[0,1]` is `2^(0. 4)` (b) `2^(-0. 4)` 1 (d) `2^(0. 6)`

The maximum value of the function f(x)=(1+x)^(0.3)/(1+x^(0.3)) in [0,1] is

For x>=0, the smallest value of the function f(x)=(4x^(2)+8x+13)/(6(1+x)), is

Let k and K be the minimum and the maximum values of the function f(x)=((1+x)^(0.6))/(1+x^(0.6)), and x in[0,1] respectively,then the ordered pair (k,K) is equal to

The value of c in Lagrange's theorem for the function f(x)={x cos((1)/(x)),x!=0 and 0,x=0 in the interval [-1,1] is

[" The maximum value of function "(x)=(|x|-2-x^(2))/(|x|+1)" lies in the interval "],[[" (a) "0(-oo,0)," (B) "0(0,oo)],[" (c) "g(1,4)," (D) "0(-3,4)]]

For xge 0 , the smallest value of the function f(x)=(4x^2+8x+13)/(6(1+x)) , is ________.

The function f(x)=(|x|)/(x),x>0 is :- (1) 0 (2) 1 (3) 2 (4) -2

Using Lagrange's theorem , find the value of c for the following functions : (i) x^(3) - 3x^(2) + 2x in the interval [0,1/2]. (ii) f(x) = 2x^(2) - 10x + 1 in the interval [2,7]. (iii) f(x) = (x-4) (x-6) in the interval [4,10]. (iv) f(x) = sqrt(x-1) in the interval [1,3]. (v) f(x) = 2x^(2) + 3x + 4 in the interval [1,2].

The function f(x)=x^(x) decreases on the interval (a) (0,e)(b)(0,1)(c)(0,1/e)(d)(1/e,e)

Statement - 1 : Rolle's Theorem can be applied to the function f(x)=1+(x-2)^(4//5) in the interval [0, 4] and Statement - 2 : f(x) is continuous in [0, 4] and f(0)=f(4) .