Value of f′(6) in given polynomialA polynomial function f(x) of degree 5 with leading coefficients one , increase in the interval ( − ∞ , 1 ) and ( 3 , ∞ ) and decrease in the interval (1,3). Given that f ′ ( 2 ) = 0 , f ( 0 ) = 4.Then value of f ′ ( 6 ) =Attempt: Given function increase in the interval ( − ∞ , 1 ) and ( 3 , ∞ ) and decreasein the interval (1,3). So we have f ′ ( 1 ) = 0 and f ′ ( 3 ) = 0.So f ′ ( x ) = ( x − 1 ) ( x − 2 ) ( x − 3 ) ( x − α ).Could some help me how i calculate α ,

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Value of f′(6) in given polynomialA polynomial function f(x) of degree 5 with leading coefficients one , increase in the interval  (  −  ∞  ,  1  ) and   (  3  ,  ∞  ) and decrease in the interval (1,3). Given that       f    ′    (  2  )  =  0    ,  f  (  0  )  =  4.Then value of       f    ′    (  6  )  =Attempt: Given function increase in the interval   (  −  ∞  ,  1  ) and   (  3  ,  ∞  ) and decreasein the interval (1,3). So we have       f    ′    (  1  )  =  0 and       f    ′    (  3  )  =  0.So       f    ′    (  x  )  =  (  x  −  1  )  (  x  −  2  )  (  x  −  3  )  (  x  −  α  ).Could some help me how i calculate   α  ,

Cassie Moody · Accepted Answer

Step 1Since f decreases on the entire interval (1,3), the root of f′ at 2 must have even multiplicity. It cannot be 4-fold or more (since that would make the degree of f′ as a polynomial too high), so it must be a double root, and your   α  =  2.Step 2Note also that the leading coefficient of f′ is 5, which you had forgotten in your development.

Valentina Holland · Accepted Answer

Step 1  f  (  x  )  =      x    5    +  a      x    4    +  b      x    3    +  c      x    2    +  d  x  +  4      f    ′    (  2  )  =  80  +  32  a  +  12  b  +  4  c  +  d  =  0      f    ′    (  1  )  =  5  +  4  a  +  3  b  +  2  c  +  d  =  0      f    ′    (  3  )  =  405  +  108  a  +  27  b  +  6  c  +  d  =  0      f    ′    (  6  )  =      5.6    4    +      4.6    3    .  a  +      3.6    2    b  +  12  c  +  d

A polynomial function f(x) of degree 5 with leading coefficients one, increase in the interval (-infty, 1) and (3,infty) and decrease in the interval (1, 3). Given that f′(2)=0,f(0)=4. Then value of f′(6)=?

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