Maxima and MinimaMedium
Question
If f(x) = x3 + ax2 + bx + c is minimum at x = 3 and maximum at x = -1, then-
Options
A.a = -3, b = -9, c = 0
B.a = 3, b = 9, c = 0
C.a = -3, b = -9, c ∈ R
D.none of these
Solution
f(x) = x3 + ax2 + bx + c
f′(x) = 3x2 + 2ax + b
f′(x) = 0
3x2 + 2ax + b = 0 .... (1)
get the two roots but given x = 3 for min.
and x = -1 for max.
so eq. (x - 3) (x + 1) = 0
x2 - 2x - 3 = 0 ..... (2)
Eq. (1) and (2) are same
3x2 + 2ax + b = 0
x2 +
and x2 - 2x - 3 = 0
= -2; 
= -3
a = -3 ; b = -9
and c ∈ R
so a = -3; b = -9 c ∈ R
f′(x) = 3x2 + 2ax + b
f′(x) = 0
3x2 + 2ax + b = 0 .... (1)
get the two roots but given x = 3 for min.
and x = -1 for max.
so eq. (x - 3) (x + 1) = 0
x2 - 2x - 3 = 0 ..... (2)
Eq. (1) and (2) are same
3x2 + 2ax + b = 0
x2 +
and x2 - 2x - 3 = 0
= -2; = -3a = -3 ; b = -9
and c ∈ R
so a = -3; b = -9 c ∈ R
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