Q. 14.6( 5 Votes )

# Show that ƒ(x) = x^{3} is continuous as well as differentiable at x=3.

Answer :

Given:

f(x) = x^{3}

If a function is differentiable at a point, it is necessarily continuous at that point.

Left hand derivative (LHD) at x = 3

Right hand derivative (RHD) at x = 3

LHD = RHD

Therefore, f(x) is differentiable at x = 3.

Also, f(3) =27

Therefore, f(x) is also continuous at x = 3.

Rate this question :

Show that of all the rectangles of given area, the square has the smallest perimeter.

Mathematics - Board PapersFind the value of a and b such that the following function f(x) is a continuous function:

Mathematics - Board Papers

If x sin (a + y) + sin a cos (a + y) = 0, prove that

Mathematics - ExemplarThe function f(x) = e^{|x|} is

Show that of all the rectangles with a given perimeter, the square has the largest area.

Mathematics - Board PapersIf the function f (x) given by

is continuous at x =1, find the values of a and b.

Mathematics - Board PapersFind when x and y are connected by the relation given

(x^{2} + y^{2})^{2} = xy

Let f(x) = |sinx|. Then

Mathematics - ExemplarThe derivative of cos^{-1}(2x^{2} – 1) w.r.t. cos^{-1} x is