Suppose that y=f(x) has a maximum at x=x_0. The value of the second-order derivative evaluated at this point, i.e. f''(x_0), will be :
a) negative
b) zero
c) positive
d) it is not possible to tell. It could be positive , negative or equal to zero

Question

Suppose that y=f(x) has a maximum at x=x_0. The value of the second-order derivative evaluated at this point, i.e. f''(x_0), will be :
a) negative
b) zero
c) positive
d) it is not possible to tell. It could be positive , negative or equal to zero

anonymous · Answer

Second derivative test:
If f''(x) < 0, then f has a local maximum at point x.
Therefore the value of f''(x_0) will be negative.

anonymous · Answer

how about if the situation is first order?

anonymous · Answer

is will be zero?

anonymous · Answer

in order for the second derivative test to work, f'(x) = 0, due to it being a critical point for the equation