Show that `f(x)=5x-4` , `0< x < 1` `f(x)=4x^3-3x` , `1< x <2` continuous at `x=1`

Show that f(x)={5x-4, when 0

Show that f(x)={5x-4 , when 0ltxle1, 4x^3-3x , when 1ltxlt2 is continuous at x=1.

Show that f(x) = {:{(5x-4, when, 0 lt x le 1), (4x^(2) - 3x, when, 1 lt x lt 2):} is continuous at x = 1 .

Show that f(x) = x^5 - 5x^4 + 5x^3 - 1 has a local maximum at x = 1, a local minimum at x = 3 and neither at x = 0

If f(x)=|x-2|+|x-4| show that f'(3) = 0

Show that f(x) = ( x tan 2x)/(sin 3x sin 5x), x ne 0, f (0) = (2)/(15) is continous at x = 0 .

(i) Show that f (x) = x ^( 4//3) is differentiable at x = 0 , and hence find f ' (0) . (ii) Show that g(x) = x ^( 3//2) is not differentiable at x = 0

Show that f(x) = x sin ((1)/(x)), x ne 0 , f(0) = 0 is continuous at x = 0

Show that f (x) = f(x) = {(x,sinfrac(1)(x)),(0,x=0):} is continuous at x = 0