If a function `f(x)` has `f^(prime)(a)=0a n df^(a)=0,` then (a) `x=a` is a maximum for `f(x)` (b)`x=a` is a minimum for `f(x)` (c)can not conclude anything about its maxima and minima (d)`f(x)` is necessarily a constant function.

If f(x)=m x+ca n df(0)=f^(prime)(0)=1. What is f(2)?

If for a function f(x),f^'(a)=0,f^(' ')(a)=0,f^(''')(a)>0, then at x=a ,f(x) has a (a) minimum value (b) maximum value (c)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^(ii) (c)=f^(iii) (c)=f^(iv) (c)=f^v(c)=0. Then f (a)has a local extermum at x=cdot f (b)has neither local maximum nor minimum at x=c f (c)is necessarily a constant function (d)it is difficult to say whether a)or(b)dot

A function f such that f'(a)=f''(a)=….=f^(2n)(a)=0 , and f has a local maximum value b at x=a ,if f (x) is

The function f(x)= xcos(1/x^2) for x != 0, f(0) =1 then at x = 0, f(x) is

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

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

Let f(x) be a cubic function such that f'(1)=f''(2)=0 . If x=1 is a point of local maxima of f(x), then the local minimum value of f(x) occurs at

A polynomial function f(x) is such that f'(4)= f''(4)=0 and f(x) has minimum value 10 at x=4 .Then

Let f(x) be a function defined as follows: f(x)=sin(x^2-3x),xlt=0; and 6x+5x^2,x >0 Then at x=0,f(x) (a) has a local maximum (b) has a local minimum (c) is discontinuous (d) none of these