If `f(x)` is continuous and differentiable on R and its derivative vanishes for 2 values of x only. Then `f(x)` cannot vanish for more than ........ points.

Show that f (x) = | x - 2 | is continuous but not differentiable at x = 2 .

Show that the function f(x) =x^2 is continuous and differentiable at x=2.

If f(x)=|ln|x|, then (a)f(x) is continuous and differentiable for all x in its domain (b) f(x) is continuous for all for all x in its domain but not differentiable at x=+-1 (c) f(x) is neither continuous nor differentiable at x=+-1 (d) none of these

If f(x)=|(log)_e|x| , then f(x) is continuous and differentiable for all x in its domain] (b) f(x) is continuous for all x in its domain but not differentiable at x=+-1 (c) f(x) is neither continuous nor differentiable at x=+-1 (d) none of these

Explain whether f(x) is continuous and has a derivative at the point x=1 were f(x)=x for 0 1

If the derivative of an odd cubic polynomial vanishes at two different values of ‘x’ then

If y=f(x) is differentiable at x=a; then it is not necessary that the derivative is continuous at x=a