Question

What is the concavity of a linear function?

Answer 1

Here's an approach...

Explanation:

Let's see...

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. (You knew that!)

We can find the concavity of a function by finding its double derivative (`f''(x)`) and where it is equal to zero.

Let's do it then!

`f(x)=mx+b`

`=>f'(x)=m*1*x^(1-1)+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.