At what point does the function
f(x)=(ax+b)/(cx+d)
has no maxima or minima
1It's clearly visible that function f(x) has no criticaql points, so no maxima and minima at all points
JOIN TERRORISM AND CLEAR IIT JEE WITH AIR 1-100 FOR SURE. FOR FURTHER DETAILS, JUST CONTACT THE UNDERSIGNED.
11Let's check the derivative.....
f'(x)=ad-bcD2
D stands for the denominator.....
since f'(x) ≠0.....coz that will obviously make f(x) a const. function, let us have f'(x)>0
That gives f(x1)>f(x2)
if x1>x2
So maxima should be at infinity.....but when x→∞, f'(x)→0, thus function becomes const = ac
Same argument when f'(x)<0......
1If ad≠bc,
at all points of the domain of definition of the function of the derivative retains its sign.
If bc=ad,
then the function is a constant.
Hence the answer.
