Feb 21, 2018
edited by Guest  Feb 21, 2018

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



cool cool cool

 Feb 21, 2018

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 

 Feb 21, 2018

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