Determine antiderivative of f.So I have a function: f ( t ) = { − 1 , if − 2 ≤ t ≤ 0 2 − t 2 − 6 t + 9 , if 0 &lt; t &lt; 6 − 1 , if 6 ≤ t ≤ 8 I need to find the antiderivative of f(t) on the interval: − 2 &lt; t &lt; 8.And I need to investigate whether the antiderivative has a maximum value on the interval.So far I've figured out that the second function 2 − t 2 − 6 t + 9 can be described as an absolute value: 2 − | t − 3 |.That makes it 4 different functions in total that describes f(t)However, I'm not sure exactly how to formulate a function for the antiderivative on the given interval.

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Determine antiderivative of f.So I have a function:  f  (  t  )  =      {                            −          1          ,                          if                       −            2                    ≤          t          ≤          0                                      2          −                                    t              2                        −            6            t            +            9                    ,                          if           0          &amp;lt;          t          &amp;lt;          6                                      −          1          ,                          if           6          ≤          t          ≤          8                        I need to find the antiderivative of f(t) on the interval:   −  2  &amp;lt;  t  &amp;lt;  8.And I need to investigate whether the antiderivative has a maximum value on the interval.So far I&#039;ve figured out that the second function   2  −            t      2        −    6    t    +    9   can be described as an absolute value:   2  −  |      t    −    3    |.That makes it 4 different functions in total that describes f(t)However, I&#039;m not sure exactly how to formulate a function for the antiderivative on the given interval.

Leslie Rollins · Accepted Answer

Step 1First let&#039;s be explicit about what you say you already figured out:  f  (  t  )  =      {                            −          1          ,                          if                       −            2                    ≤          t          ≤          0                                      t          −          1          ,                          if           0          &amp;lt;          t          ≤          3                                      5          −          t          ,                          if           3          &amp;lt;          t          &amp;lt;          6                                      −          1          ,                          if           6          ≤          t          ≤          8                        Step 2  F  (  x  )  =      {                                                          ∫                          −              2                        x                    f          (          t          )                    d          t                                  if                       −            2                    ≤          x          ≤          0          ,                                                                    ∫                          −              2                        0                    f          (          t          )                    d          t          +                      ∫            0            x                    f          (          t          )                    d          t                                  if           0          ≤          x          ≤          3          ,                                                                    ∫                          −              2                        0                    f          (          t          )                    d          t          +                      ∫            0            3                    f          (          t          )                    d          t          +                      ∫            3            x                    f          (          t          )                    d          t                                  if           3          ≤          x          ≤          6          ,                                              and so on.                        Note that here I&#039;ve written   “      ≤    &#039;&#039; rather than   “      &amp;lt;    &#039;&#039; since altering the value of f at isolated points does not affect the integral.

Determine antiderivative of f. So I have a function: f ( t ) = { <mt

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