Finding f with the given information, antiderivatives?Find f. f ″ ( t ) = 3 / t f ( 4 ) = 12 f ′ ( 4 ) = 5I'm not quite sure how I am supposed to find f with this information.

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Finding f with the given information, antiderivatives?Find f.      f    ″    (  t  )  =  3      /        t    f  (  4  )  =  12      f    ′    (  4  )  =  5I&#039;m not quite sure how I am supposed to find f with this information.

humbast2 · Accepted Answer

Step 1Hint: Integrate f′′ to find f′ up to an additive constant.Then use the fact that you are told       f    ′    (  4  )  =  5 to find the specific additive constant.Then, repeat the process: integrate this specific f′ to find f up to another additive constant.Step 2Finally, use the fact that you are told   f  (  4  )  =  12 to find this additive constant.As an example, if you know   f  (  x  )  =  5      x    2    +  C, and you know   f  (  1  )  =  3, then   5  (  1      )    2    +  C  =  3, so   C  =  −  2.

Jaqueline Kirby · Accepted Answer

Explanation:            d      [              f        ′            (      t      )      ]              d      t        =  3      t          −              1        2                ⟹    d  [      f    ′    (  t  )  ]  =  3      t          −              1        2              d  tIntegrating either sides       f    ′    (  t  )  =  3            t                        1          2                            1      2        +  K  =  6      t                  1        2              +  K where K is an arbitrary constant and as   ∫      x    m       d  x  =                    x                  m          +          1                            m        +        1              +  K for   m  +  1  ≠  0  5  =      f    ′    (  4  )  =  6  ⋅      4                  1        2              +  K    ⟹    K  =  ?

Finding f with the given information, antiderivatives? Find f. f ″ </msup

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