Show that the function f(x) = is continuous at x = 1 but not differentiable.
Given, f(x) = is continuous at x = 1
f(x) is continuous at x = 1
Now differentiable at x = 1
R.H.D. at x = 1 =
=
=
=
L.H.D. at x = 1 =
=
= 2
f(x) is not differentiable at x = 1
Find the points on the curve 4x3 - 3x + 5 at which the equation of the tangent is parallel to the x-axis.
The population of a town grows at the rate of 10% per year. Using differential equation, find how long will it take for the population to grow 4 times.