What is the concavity of a linear function?

Kennedy Ford

Kennedy Ford

Answered question

2022-04-16

What is the concavity of a linear function?

Answer & Explanation

Ausspruchx807

Ausspruchx807

Beginner2022-04-17Added 6 answers

Step 1
A linear is in the form f(x)=mx+b where m is the slope, x is the variable, and b is the y-intercept.
We can find the concavity of a function by finding its double derivative (f(x)) and where it is equalto zero
Let's do it then
f(x)=mx+b
f(x)=m×1×x11+0
f(x)=m×1
f(x)=m
f(x)=0
So this tells us that linear functions have to curve at every given point.
Knowing that the graph of linear functions is a straight line, this does not make sense, does it?
Therefore, there is no point of concavity on the graphs of linear functions.

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