Statement 1: Let `f(x)=5-4(x-2)^(2/3)dot` Then at `x=2,` the function `f(x)` attains neither the least value nor the greatest value. Statement 2: At `x=2,` then first derivative does not exist.

Prove that the function f(x)=x^2-x+1 is neither increasing nor decreasing on (-1,\ 1) .

Statement 1: Leg f(x)=x[x]a n d[dot] denotes the greatest integral function, when x is not an integer, then rule for f^(prime)(x) is given by [x]dot Statement 2: f^(prime)(x) does not exist for any x integer. (a)Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1. (b)Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1. (c)STATEMENT 1 is TRUE and STATEMENT 2 is FALSE. (d)STATEMENT 1 is FALSE and STATEMENT 2 is TRUE.

Let f(x)=(x^(2)+2)/([x]),1 le x le3 , where [.] is the greatest integer function. Then the least value of f(x) is

Let f(x)=(x^3-6x^2+12 x-8)e^xdot Statement 1: f(x) is neither maximum nor minimum at x=2. Statement 2: If a function x=2 is a point of inflection, then it is not a point of extremum.

Statement-1 : Let f(x) = |x^2-1|, x in [-2, 2] => f(-2) = f(2) and hence there must be at least one c in (-2,2) so that f'(c) = 0 , Statement 2: f'(0) = 0 , where f(x) is the function of S_1

The least value of the function f(x)= 2cosx +x in the closed interval [0,pi/2] is: A. 2 B. pi/6 + sqrt3 C. pi/2 D. The least value does not exist

Show that the function f(x)=(x-a)^2(x-b)^2+x takes the value (a+b)/2 for some value of x in [a , b]dot

Statement -1 The maximum value of f(x)=1/(3x^4+8x^3-18x^2+60) "is"1/(53) Statement -2 : The function g(x) = 1/(f(x)) attains its minimum value at x=1 and x=-3

Statement I For the function f(x)={:{(15-x,xlt2),(2x-3,xge2):}x=2 has neither a maximum nor a minimum point. Statament II ff'(x) does not exist at x=2.

Statement 1: Let f: RvecR be a real-valued function AAx ,y in R such that |f(x)-f(y)|<=|x-y|^3 . Then f(x) is a constant function. Statement 2: If the derivative of the function w.r.t. x is zero, then function is constant.