If for a function `f(x),f^'(a)=0,f^(' ')(a)=0,f^(a)>0,` then at `x=a ,f(x)` is minimum (b) maximum not an extreme point (d) extreme point

If a function f(x) has f^(prime)(a)=0a n df^(a)=0, then x=a is a maximum for f(x) x=a is a minimum for f(x) it is difficult to say (a)a n d(b) f(x) is necessarily a constant function.

If for a function f : R to R f (x +y ) =F(x ) + f(y) for all x and y then f(0) is

Let f(x)={(|x|,for 0 (a) a local maximum (b) no local maximum (c) a local minimum (d) no extremum

If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2a n dy(x)=f(e^x)e^(f(x)) , then y^(prime)(0) is equal to a. 1 b. 2 c. 0 d. none of these

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AAx , y in R and f(0)!=0 , then (a) f(x) is an even function (b) f(x) is an odd function (c) If f(2)=a ,then f(-2)=a (d) If f(4)=b ,then f(-4)=-b

Evaluate int_(0)^(a)(f(x))/(f(x)+f(a-x)) dx.

Consider the real function f(x ) = ( x+2)/( x-2) prove that f(x) f(-x) +f(0) =0

If f: RvecR is an odd function such that f(1+x)=1+f(x) and x^2f(1/x)=f(x),x!=0 then find f(x)dot

If f'(x)=f(x)+int_(0)^(1)f(x)dx ,given f(0)=1 , then the value of f(log_(e)2) is