If a function `f(x)` has `f^(prime)(a)=0 and f^(primeprime)(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 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

Let f:[a-> b] 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

Prove that the functions do not have maxima or minima: f(x) = e^(x)

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

If f: RtoRa n dg: RtoR are two functions such that f(x)+f^(primeprime)(x)=-xg(x) f^(prime)(x) and g(x)>0AAx in Rdot Then the function f^2(x)+(f'(x))^2 has (a)a maxima at x=0 (b)a minima at x=0 (c)a point of inflexion at x=0 (d)none of these

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)

Find the number of points of maxima and minima of the function. f(x)=1/8"In"x-bx+x^2,xgt0 where bge0 is a constant.

Let f be a real valued function satisfying f(x)+f(x+4)=f(x+2)+f(x+6) Prove that int_(x)^(x+8)f(t)dt is a constant function.

If a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, then find the value of int_0^a(dx)/(1+f(x))