`L e tf(x)={((x-1)(6x-1))/(2x-1),ifx!=1/2 0,ifx=1/2` Then at `x=1/2,` which of the following is/are not true? (a)`f` has a local maxima (b)`f` has a local minima (c)`f` has an inflection point. (d)`f` has a removable discontinuity.

Find the points at which the function f given by f (x) = (x-2)^(4)(x+1)^(3) has (i) local maxima (ii) local minima (iii) point of inflexion

Find all points of local maxima and local minima of the function f given by f(x) = x^(3) – 3x + 3.

Find all the points of local maxima and local minima of the function f given by f(x) = 2x^( 3) – 6x^(2) + 6x +5.

Find all the points of local maxima and local minima of the function f given by f(x) = 2x^(3) – 6x^(2) + 6x +5.

f(x)=4tanx-tan^2x+tan^3x ,x!=npi+pi/2, (a)is monotonically increasing (b)is monotonically decreasing (c)has a point of maxima (d)has a point of minima

For the function f(x)=(e^x)/(1+e^x), which of the following hold good? f is monotonic in its entire domain. Maximum of f is not attained even though f is bounded f has a point of inflection. f has one asymptote.

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

Consider the function f:(-oo,oo)vec(-oo,oo) defined by f(x)=(x^2+a)/(x^2+a),a >0, which of the following is not true? maximum value of f is not attained even though f is bounded. f(x) is increasing on (0,oo) and has minimum at ,=0 f(x) is decreasing on (-oo,0) and has minimum at x=0. f(x) is increasing on (-oo,oo) and has neither a local maximum nor a local minimum at x=0.

The function f(x)=2|x|+|x+2|-||x+2|-2|x|| has a local minimum or a local maximum at x equal to:

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^+)