Let `f(x)={sin(pix)/2,0lt=x<1 3-2x ,xgeq1` `f(x)` has local maxima at `x=1` `f(x)` has local minima at `x=1` `f(x)` does not have any local extrema at `x=1` `f(x)` has a global minima at `x=1`

The function f(x)= x/2 + 2/x ​ has a local minimum at

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 (A) the distance between (-1,2)a n d(af(a)), where x=a is the point of local minima is 2sqrt(5) (B) f(x) is increasing for x in [1,2sqrt(5]) (C) f(x) has local minima at x=1 (D)the value of f(0)=15

let f(x)=(x^2-1)^n (x^2+x-1) then f(x) has local minimum at x=1 when

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^+)

Let f(x) be defined as f(x)={tan^(-1)alpha-5x^2,0ltxlt1 and -6x ,xgeq1 if f(x) has a maximum at x=1, then find the values of alpha .

Let f(x) ={underset(x^(2) +xb " " x ge1)(3-x " "0le x lt1). Find the set of values of b such that f(x) has a local minima at x=1.

Let f(x) be a polynomial of degree 3 such that f(-2)=5, f(2)=-3, f'(x) has a critical point at x = -2 and f''(x) has a critical point at x = 2. Then f(x) has a local maxima at x = a and local minimum at x = b. Then find b-a.

The function f(x) = (x)/( 2) + (2)/( x) has a local minimum at

Find all the points of local maxima and local minima as well as the corresponding local maximum and local minimum values for the function f(x)=(x-1)^3(x+1)^2 .

If f(x) is a cubic polynomil which as local maximum at x=-1 . If f(2)=18,f(1)=-1 and f'(x) has minimum at x=0 then