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(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

Lert f:[a , b]vec be a function such that for c in (a , b),f^(prime)(c)=f^"(c)=f^"'(c)=f^(i v)(c)=f^v(c)=0. Then f (a)has a local extermum at x=c dot (b) f has neither local maximum nor minimum at x=c (c) f is necessarily a constant function (d)it is difficult to say whether (a)or(b)dot

Let f: R->R be a differentiable function for all values of x and has the property that f(x)a n df^(prime)(x) has opposite signs for all value of xdot Then, (a) f(x) is an increasing function (b) f(x) is an decreasing function (c) f^2(x) is an decreasing function (d) |f(x)| is an increasing function

If f(x)=|x a a a x a a a x|=0, then f^(prime)(x)=0a n df^(x)=0 has common root f^(x)=0a n df^(prime)(x)=0 has common root sum of roots of f(x)=0 is -3a none of these

Let f(x) be a function defined as follows: f(x)=sin(x^2-3x),xlt=0; a n d6x+5x^2,x >0 Then at x=0,f(x) has a local maximum has a local minimum is discontinuous (d) none of these

If function f satisfies the relation f(x)*f^(prime)(-x)=f(-x)*f^(prime)(x) for all x ,

Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then f(x) is an increasing function in (0,oo) f(x) is a decreasing function in (-oo,oo) f(x) is an increasing function in (-oo,oo) f(x) is a decreasing function in (-oo,0)

Let a function f be defined by f(x)=(x-|x|)/x for x ne 0 and f(0)=2. Then f is

A function y=f(x) satisfies (x+1)f^(prime)(x)-2(x^2+x)f(x)=(e^x^2)/((x+1)),AAx > -1. If f(0)=5, then f(x) is

If f(x)=int(x^8+4)/(x^4-2x^2+2)dxa n df(0)=0,t h e n f(x) is an odd function f(x) has range R f(x) has at least one real root f(x) is a monotonic function.