#1**+1 **

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

CPhill
Feb 21, 2018

#2**+1 **

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

ElectricPavlov
Feb 21, 2018