Question 912785
This function's interval of [0,6] has been split up into these two intervals: [1,3] and [3,5]


It turns out that the slopes of the secant lines will be decreasing in a concave down section of a graph. It's somewhat connected to the idea that the tangent line slopes are decreasing.


Since the interval [1,3] is to the left of [3,5], this means (f(3)-f(1))/(3-1) will be larger. Both slopes are negative, but (f(3)-f(1))/(3-1) is closer to 0, therefore larger.


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Imagine the flip scenario: say  (f(5)-f(3))/(5-3) is larger. This would mean that the slopes are increasing, but this would mean you're on a concave up section of the graph. So this contradicts what we're given.


Hopefully it's making sense.


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Thanks,


Jim