Which of these values for $f(12)$ are possible? If  $f(10)=30, f'(10)=-2$ and $f''(x)<0$ for $x \geq 10$, which of the following are possible values for $f(12)$ ? There may be more than one correct answer.
$24, 25, 26, 27, 28$
So since $f''(x)<0$ indicates that the graph for $f(x)$ is concave down, and after using slope formula I found and answer of $26$, would that make $f(12)$ less than or equal to $26$? Thank you! 

Hint: The second derivative condition tells you that the first derivative is decreasing past $10$, and so is $\lt -2$ past $10$.  
By the Mean Value Theorem, $\dfrac{f(12)-f(10)}{12-10}=f'(c)$ for suitable $c$ strictly between $10$ and $12$. Now test the various suggested values.    
For example, $\dfrac{27-30}{12-10}=-1.5$, impossible.
