At x = 3, the function given by f(x) = { x² , x<3} ; {6x-9 , x ≥ 3} is

Question

a. continuous but not differentiable.

b. differentiable but not continuous.

c. neither continuous nor differentiable.

d. both continuous and differentiable.

Answer 1

lim(x→3-) = 3^2 = 9
lim(x→3+) = 6*3-9 = 9
so f(x) is continuous

now check f' and see whether it is also the same from both sides.