Please help me understand the concept of concavity and slope

Indranil

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Feb 22, 2018
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1. If the graph is concave (curved upward), the slope is increasing.

2. If the graph is concave downward (curved downward), the slope is decreasing.

I can't understand the two concepts above clearly, Could you get them easier, please?
 
1. If the graph is concave (curved upward), the slope is increasing.

2. If the graph is concave downward (curved downward), the slope is decreasing.

I can't understand the two concepts above clearly, Could you get them easier, please?

Take a look at the pictures here (after Definition 1): Paul's Online Math Notes. What you see there is that as you move from left to right on a concave up graph, the slope is increasing (in the first example, from -3 to -2 to -1, and in the second, from 1 to 2 to 3, or whatever the numbers might actually be). Similarly, in the concave down graphs, as you move to the right the slope decreases, from 0 to increasingly negative on the left, and from positive down toward zero on the right.

Possibly you are missing the fact that we are talking about signed slopes, so that a line with negative slope becomes less steep as the slope increases (toward zero).

Does that help? If not, tell us more specifically what confuses you.
 
Take a look at the pictures here (after Definition 1): Paul's Online Math Notes. What you see there is that as you move from left to right on a concave up graph, the slope is increasing (in the first example, from -3 to -2 to -1, and in the second, from 1 to 2 to 3, or whatever the numbers might actually be). Similarly, in the concave down graphs, as you move to the right the slope decreases, from 0 to increasingly negative on the left, and from positive down toward zero on the right.

Possibly you are missing the fact that we are talking about signed slopes, so that a line with negative slope becomes less steep as the slope increases (toward zero).

Does that help? If not, tell us more specifically what confuses you.
Thank you very much. Now I got it.
 
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