b):}`.
Then

Let `f: [a, b] -> [1,oo)`, be a continuous function and let `g: R -> R` be defined as

`g(x)={(0,if x<a),(int_a^x f(t)dt ,if a<=x<=b),(int_a^bf(t)dt ,if x>b):}`.

Then

g(x) is continuous but not differentiable at 'a'

g(x) is differentiable on R

g(x) is discontinuous at 'b'

g(x) is continuous and differentiable at either 'a' or ‘b' but not both.

Let `f: [a, b] -> [1,oo)`, be a continuous function and let `g: R -> R` be defined as`g(x)={(0,if x<a),(int_a^x f(t)dt ,if a<=x<=b),(int_a^bf(t)dt ,if x>b):}`.Then