What is the concavity of a linear function?

1 Answer
Jun 10, 2018

Answer:

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.