What can you conclude from the following information: f(6) = 7, f'(6) = 0, f"(6) = −3?

Question

What can you conclude from the following information: f(6) = 7, f'(6) = 0, f"(6) = −3?

Answer 1

Since f(6) = 7 and f'(6) = 0, the graph of y = f(x) has a horizontal tangent at the point (6,7).

Since f"(6) = -3 < 0, the graph of y = f(x) is concave down in the vicinity of (6,7).

So, y = f(x) has a relative maximum at the point (6,7).

Answer 2

Either the person who devised this problem made a mistake or you copied the problem wrong. Once you get to a derivative that equals zero, any further derivatives are also zero. you can't go from f'(6)=0 to f"(6)=-3. It's a contradiction.

You can conclude the information is wrong.

You can go from f(6) = 7 to f'(6) = 0, since the derivative of any constant is zero. But zero is also a constant and taking the 2nd derivative should also =0