Question

Why is the answer E?

Answer 1

E

Explanation:

For a function to be differentiable at a point, it must be continuous at that point [ f(x⁻) = f(x⁺) ], and smooth at that point [ f'(x⁻) = f'(x⁺) ].

f(-1⁻) = 3(-1) + 5 = 2

f(-1⁺) = -(-1)² + 3 = 2

So the function is continuous.

f'(-1⁻) = 3

f'(-1⁺) = -2(-1) = 2

So the function is not smooth.

Therefore, the derivative f'(-1) does not exist.