Antiderivative HelpI am trying to find f(x) if I know that f ″ ( x ) = − 2 + 12 x − 12 x 2 , f ( 0 ) = 4 , f ′ ( 0 ) = 12First I found the first derivative f ′ ( x ) = − 2 x + 6 x 2 − 4 x 3 + C.and then I found the function, which is: f ( x ) = − x 2 + 2 x 3 − x 4 + C x + DNow I am lost as to what to do with those values they gave me f ( 0 ) = 4 , f ′ ( 0 ) = 12.

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Antiderivative HelpI am trying to find f(x) if I know that      f    ″    (  x  )  =  −  2  +  12  x  −  12      x    2    ,      f  (  0  )  =  4  ,         f    ′    (  0  )  =  12First I found the first derivative       f    ′    (  x  )  =  −  2  x  +  6      x    2    −  4      x    3    +  C.and then I found the function, which is:  f  (  x  )  =  −      x    2    +  2      x    3    −      x    4    +  C  x  +  DNow I am lost as to what to do with those values they gave me   f  (  0  )  =  4  ,         f    ′    (  0  )  =  12.

Jaylee Dodson · Accepted Answer

Step 1After finding the value of f′(x) with the unknown constant C, use the fact that       f    ′    (  0  )  =  12 to determine the value of C. That is, since       f    ′    (  x  )  =  −  2  x  +  6      x    2    −  4      x    3    +  C    and        f    ′    (  0  )  =  12 that means that   12  =      f    ′    (  0  )  =  −  2  (  0  )  +  6  (  0      )    2    −  4  (  0      )    3    +  C  ..Step 2This should tell you the value of C.Then find f(x), which will give you another unknown constant D. Use the fact that   f  (  0  )  =  4 to figure out the value of D.

Antiderivative Help I am trying to find f(x) if I know that f ″ </msup>

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