Necessary Condition for an Extrema(Is a Function Differentiable at Boundaries)

Q. The necessary condition to be maximum or minimum for the function is

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) = -ve

Q.

If f(x) and f’(x) are differentiable at x = c, then the necessary condition for f(c) to be an extremum of f(x) is -

1. f(c) = 0

2. f’(c) = 0

3. f”(c) = 0

4. None of these

Q. The necessary condition to be maximum or minimum for the function is

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) = -ve

Q. Suppose $f\left(x\right)=x^3+a{x}^2+bx+c$ satisfies $f(–2)=-10$ and takes the extreme value $\frac{50}{27}$ at $x=\frac{2}{3}.$ Then the value of $a+b+c$ is