Question

state the necessary and sufficient conditions of maximum and minimum values of the function Y = f(x)​

Answer 1

Answer:

1) f’(x) = 0 and it is sufficient

2) f’’(x) = 0 and it is sufficient

3) f’(x) = 0 but it is not sufficient

4) f’(x) = 0 and f’’(x) = – vet

Solution: (3) f’(x) = 0 but it is not sufficient

Step-by-step explanation:

The necessary condition to be maximum or minimum of the function f’ (x) = 0 and for maximum f’’ (x) = negative and for minimum f’’ (x) = positive.

Hence f’ (x) = 0, but it is not sufficient

Answer 2

Solution: (3) f’(x) = 0 but it is not sufficient

The necessary condition to be maximum or minimum of the function f’ (x) = 0 and for maximum f’’ (x) = negative and for minimum f’’ (x) = positive.

Hence f’ (x) = 0, but it is not sufficient