(a, b, c)

The domain of definition of this function is the interval –1 ≤ x ≤ 1, because, for f to be defined, we must have 1 –x 2 ≥ 0.

∴ f ′ (x) = . (2x)

at x ≠ 0 and x ≠ ± 1. As x → 1 – or x → – 1+, we have f ′ (x) → ∞ . To find out whether the derivative f ′ (x) exists at the point x = 0, we note that

f ′ (0+) =

=

=

= =

Similarly f ′ (0 – ) = –

Hence f has no derivative at x = 0

Since for a continuous function h(x) with h(x) ≥ 0, the function g(x) = is continuous. So f is continuous on [–1, 1] in particular at x = 0