Help with function

Well....we could use average rates of change, but here's something that's faster

Using the function ..... 24x - 10

Setting this to 0 and solving for x we get that x  = 10/24   = 5/12

This function be negative for all x values < 5/12.....so our given function will be concave down for all the same x values

For all x values > 5/12, this function will be positive so our given function will be concave up for the same x values

So....on the interval  [ -10, -6 ]....the given  function will be concave down

Here's a graph : https://www.desmos.com/calculator/5jagkhb5zl

The problem with using rates of change to calculate concavity is that we may "skip" over some interval  where the concavity changes

My take:

f '  =  12x^2 - 10x 

 f ' (-10) = 1300

 f ' (-6)   =  492   

  Both slopes are POSITIVE

      from -10  to  -6   the slope is DECREASING

           so the fxn is downward concave from  -10  to  -6