JEE Main 2020 — Application Of Derivatives Question with Solution
From: JEE Main 2020 (Online) 2nd September Morning Slot
Question
If p(x) be a polynomial of degree three that has
a local maximum value 8 at x = 1 and a local
minimum value 4 at x = 2; then p(0) is equal to :
Choose an option
Show full solutionCorrect option: C
Correct answer
C-12
Step-by-step explanation
Since p(x) has relative extreme at
x = 1 & 2
so p'(x) = 0 at x = 1 & 2
Let p'(x) = A(x – 1) (x – 2)
p(x) =
p(x) = + C ...(1)
As P(1) = 8
From (1)
8 =
48 = 5A + 5C ...(2)
Also P(2) = 4
From (1)
4 =
12 = 2A + 3C ......(3)
Form (3) & (4), C = –12, A = 24
Now p(0) = C = -12
x = 1 & 2
so p'(x) = 0 at x = 1 & 2
Let p'(x) = A(x – 1) (x – 2)
p(x) =
p(x) = + C ...(1)
As P(1) = 8
From (1)
8 =
48 = 5A + 5C ...(2)
Also P(2) = 4
From (1)
4 =
12 = 2A + 3C ......(3)
Form (3) & (4), C = –12, A = 24
Now p(0) = C = -12
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