Where is this function concave up?The function is: ( x 2 − 16 ) 6 .So I did all the relevant calculations and all my others answers about inflexion points, critical points, extreme points, concave down, increasing and decreasing intervals were correct. But my interval for concave up keeps coming up as wrong.This is the interval I calculated: ( − ∞ , − 4 ) ∪ ( − 4 , − 4 11 11 ) ∪ ( 4 11 11 , 4 ) ∪ ( 4 , ∞ )I also tried various alternative ones like: ( − ∞ , − 4 11 11 ) ∪ ( 4 11 11 , ∞ )

Question

Where is this function concave up?The function is:   (      x    2    −  16      )    6  .So I did all the relevant calculations and all my others answers about inflexion points, critical points, extreme points, concave down, increasing and decreasing intervals were correct. But my interval for concave up keeps coming up as wrong.This is the interval I calculated:  (  −  ∞  ,  −  4  )  ∪      (    −    4    ,    −                  4                  11                    11        )    ∪      (                  4                  11                    11        ,    4    )    ∪  (  4  ,  ∞  )I also tried various alternative ones like:      (    −    ∞    ,    −                  4                  11                    11        )    ∪      (                  4                  11                    11        ,    ∞    )

Brooklyn Mcintyre · Accepted Answer

Step 1you don&#039;t need to expand all the 2nd derivative      f    ′    (  x  )  =  6  (      x    2    −  16      )    5       2  x      f    ″    (  x  )  =  12  (      x    2    −  16      )    5    +  60  x  (      x    2    −  16      )    4    =  (      x    2    −  16      )    4    [  12  (      x    2    −  16  )  +  60  x  ]Step 2  (      x    2    −  16      )    4    ≥  0you can study the sign of   [  12  (      x    2    −  16  )  +  60  x  ]

Where is this function concave up? (x^2-16)^6

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