A function f satisfies the following conditions: f(5)=20, f'(5)=2, and f"(x)<0, for x>=5. Which of the following are possible values for f(7)? possible choices are 28, 20, 26, 24, 22
since f'(5) = 2 and f''(x) < 0 for x>=5 it means that 2 is the highest slope for x>=5 so the highest value for f(x) can be found with the linear approximation with slope 2 through the point 5,20 y = 20 + 2*(x-5) -> y = 20 +2x -10 - > y = 2x + 10now y(7) = 24but it cant really be 24 since the slope decreasing so I would say the possible values are 20,22
