The value of 'c' in Lagrange's mean value
theorem for f(x) = x - 2x2 - x + 4 in [0, 1] is
2) 1/2 3) 2/3
4) 1
1) 1/3
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Correct option is
B
3
4−
7
As f(x) is polynomial so it will be continuous and differentiable in [0,1].
f(x)=x
3
−4x
2
+8x+11
f(0)=11,f(1)=1−4+8+11
=16
f
′
(x)=3x
2
−8x+8
if c∈(0,11)
then f
′
(c)=3c
2
−8c+8 __(1)
Apply l.M.V.T
f
′
(c)=
1−0
f(1)−f(0)
=f(1)−f(0)
=16−11
=5 ___(II)
∴ from equation (I) & (II)
3c
2
−8c+8=5
3c
2
−8c+3=0
⇒c=
3
4−
7
←(0,1) verified
Step-by-step explanation:
hope it helps u
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