Tip:A–D to answerE for explanationV for videoS to reveal answer
The maximum value of f(x)=(x−1)2(x+1)3 is equal to 31252p3q then the ordered pair of (p,q) will be
- A.
(3,7)
- B.
(7,3)
(Correct Answer) - C.
(5,5)
- D.
(4,4)
Explanation
f(x) = (x+1)2(x−1)3
f'(x) = 2(x−1)(x+1)3+3(x+1)2(x−1)2
= (x−1)(x+1)2[2(x+1)+3(x−1)]=0
= (x−1)(x+1)2(5x−1)
x=1,−1,51
Sign chart: +−+−
At x=−1 (Min), x=51 (Max), x=1 (Min)
f(51)=(51−1)2(51+1)3
=(−54)2(56)3
=5216×5363
=5527×33
Hence, p=7,q=3.
Explanation
f(x) = (x+1)2(x−1)3
f'(x) = 2(x−1)(x+1)3+3(x+1)2(x−1)2
= (x−1)(x+1)2[2(x+1)+3(x−1)]=0
= (x−1)(x+1)2(5x−1)
x=1,−1,51
Sign chart: +−+−
At x=−1 (Min), x=51 (Max), x=1 (Min)
f(51)=(51−1)2(51+1)3
=(−54)2(56)3
=5216×5363
=5527×33
Hence, p=7,q=3.
