Concavity and Tangent Functions

  • Thread starter Strand9202
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  • #1
Strand9202
10
2
Homework Statement:
The problem is below. I was asked to explain what is meant in the circled part.
Relevant Equations:
None
Here is the problem (8b). I was asked to write out why the circled part was true.
63658155135__B50E8DE7-92CD-4EA2-B76E-74436AD82853.jpeg


I know that since the function is concave down then f"(x)<0. That is a fact. What I am having trouble with is why they can say the next part.

What I thought was L(x) is the tangent line and all tangent lines are above a concave down function, but not sure that is correct or true.
 

Answers and Replies

  • #2
Strand9202
10
2
I guess I am just lost on the last line, because I know the first 2 lines are true because of concave down.
 
  • #3
BvU
Science Advisor
Homework Helper
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It's a simple mistake.
$$L(x)\ge f(x) \quad \Rightarrow\quad L(8) \ge f(8)\quad \Rightarrow \quad f(8)\le L(8) = 1 $$q.e.d.
 

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