Let ƒ(x) = Show that ƒ(x) is continuous but not differentiable at x=1

Question

Philoid · Accepted Answer

Left hand limit at x = 1

f(x) = x is polynomial function and a polynomial function is continuous everywhere

Right hand limit at x = 1

f(x) = 2 - x is polynomial function and a polynomial function is continuous everywhere

Also, f(1) =1

As we can see that,

Therefore,

f(x) is continuous at x =1

Now,

LHD at x = 1

RHD at x = 1

As, LHD ≠ RHD

Therefore,

f(x) is not differentiable at x = 1