For the function f(x)=`{{:(,|x-3|,x ge 1),(,(x^(2))/(4)-(3x)/(2)+(13)/(4),x lt 1):}` which one of the folllowing is incorrect

Options

A. continuous and differentiable at x = 3
B. continuous at x = 3, but not differentiable at x = 3
C. continuous and differentiable everywhere
D. continuous at x = 1, but not differentiable at x = 1

Answer

B

Explanation

Clearly f(x) is not differentiable at x = 3
`underset(x to 3^(-))lim f(x) = underset(hto0)limf(3-h)`
`underset(hto0)lim|3- h- 3|=0`
` underset(hto3^(+))limf(x) = underset(h to 0)lim f(3 +h)`
`= underset(h to 0)lim|3 + h - 3| = 0`
and ` f(3) = |3-3| = 0 `
`therefore f(x)` is continuous at x = 3 .