+130071 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
+37157 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
