A calculus problem by Clera Sill

If f(x)=|x-a|^{m} |x-b|^{n}, where a and b are distinct real numbers, m and n are integers, then the incorrect statement among the following will be...

Statement 1: If both m and n are even, then f(x) should be continuous and differentiable at x=a and x=b

Statement 2: If m is even and nis odd, then f(x) should be continuous at x=a and x=b but not differentiable at x=b

Statement 3: If m is odd and n is even, then f(x) should be continuous at x=a and x=b but not differentiable at x=a

Statement 4: If both m and n are odd, then f(x) should be continuous but not differentiable at x=a and x=b