If `f(x)=int_0^x(sint)/t dt ,x >0,` then (a)`f(x)` has a local maxima at `x=npi(n=2k ,k in I^+)` (b)`f(x)` has a local minima at `x=npi(n=2k ,k in I^+)` (c)`f(x)` has neither maxima nor minima at `x=npi(n in I^+)` (d)`(f)x` has local maxima at `x=npi(n=2k +1, k in I^+)`

The function f(x)=x/2+2/x has a local minimum at x=2 (b) x=-2 x=0 (d) x=1

f(x) is cubic polynomial with f(x)=18a n df(1)=-1 . Also f(x) has local maxima at x=-1a n df^(prime)(x) has local minima at x=0 , then the distance between (-1,2)a n d(af(a)), where x=a is the point of local minima is 2sqrt(5) f(x) is increasing for x in [1,2sqrt(5]) f(x) has local minima at x=1 the value of f(0)=15

If f(x)={{:(3-x^(2)",",xle2),(sqrt(a+14)-|x-48|",",xgt2):} and if f(x) has a local maxima at x = 2, then greatest value of a is

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

Find the points of minima for f(x)=int_0^x t(t-1)(t-2)dt

The function (sin(x+a))/(sin(x+b)) has no maxima or minima if (a) b-a=npi,n in I (b) b-a=(2n+1)pi,n in I (c) b-a=2npi,n in I (d) none of these

If P(x) is a polynomial of degree 3 satisfying p(-1)=10 ,p(1)=-6a n dp(x) has maxima at x=-1a n dp^(prime)(x) has minima at x=1, find the distance between the local maxima and local minima of the curve.

If f(x)=x^3+b x^2+c x+d and 0 le b^2 le c , then a) f(x) is a strictly increasing function b)f(x) has local maxima c) f(x) is a strictly decreasing function d) f(x) is bounded

Let f:[1,oo)->R and f(x)=x(int_1^xe^t/tdt)-e^x .Then (a) f(x) is an increasing function (b) lim_(x->oo)f(x)->oo (c) fprime(x) has a maxima at x=e (d) f(x) is a decreasing function

Let f(x)=(x-1)^4(x-2)^n ,n in Ndot Then f(x) has a maximum at x=1 if n is odd a maximum at x=1 if n is even a minimum at x=1 if n is even a minima at x=2 if n is even