If `f(x)={x^2,xlt=0 2sinx ,x >0'in v e s t iga t et h e` function at `x=0` for maxima/minima

Let f(x)= {x^(3)+x^(2)+10x, xlt0 .Investigate x=0 for local -3sinx,xge0 maxima/minima.

f(x)={cos(pix)/2,x >0 x+a ,xlt=0 Find the values of a if x=0 is a point of maxima.

f(x)={cos(pix)/2,x >0, x+a ,xlt=0 Find the values of a if x=0 is a point of maxima.

If f(x+2a)=f(x-2a),t h e np rov et h a tf(x)i sp e r iod i cdot

If f(x+2a)=f(x-2a),t h e np rov et h a tf(x)i sp e r iod i cdot

Examine the continuity of the function f(x)={3x-2,\ \ \ xlt=0x+1,\ \ \ x >0 at x=0 . Also sketch the graph of this function.

if f(x)={x^3+x^2,for0lt=xlt=2x+2,for2

if f(x)= {x^3+x^2,for 0lt=xlt=2x+2 ,for2

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^+)

Find the maxima and minima of the function y=x(x-1)^2,0lt=xlt=2.