inequalities qn (2 Viewers)

[Masaken]

how would i interpret this in order to be able to get the correct answer? the worked solutions (answer is D) interpret the question geometrically but i don't really understand what they're doing. thanks in advance

 

[Drongoski]

f(x) is concave down, if f''(x) < 0, assuming a < 1 < b. (f(a)+f(b))/2 is the value of the mid-point of the line segment joining the points A(a,f(a)) and B(b,f(b)), which is below the point M((a+b)/2, f((a+b)/2)).

 

[Masaken]

f(x) is concave down. (f(a)+f(b))/2 is the value of the mid-point of the line segment joining the points A(a,f(a)) and B(b,f(b)), which is below the point M((a+b)/2, f((a+b)/2)).

oh, i see... thanks a lot, the solutions gave a diagram but i had no idea what was going on or how to use it