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Question

Let the function, f:[7,0]R be continuous on [7,0] and differentiable on (7,0). If f(7)=3 and f(x)2, for all x(7,0), then for all such functions f, f(1)+f(0) lies in the interval:

A
[6,20]
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B
(,20]
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C
(,11]
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D
[3,11]
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Solution

The correct option is B (,20]
f(7)=3 and f(x)2
Applying LMVT in [7,0], we get
f(7)f(0)7=f(c)23f(0)72f(0)+314f(0)11

Applying LMVT in [7,1], we get
f(7)f(1)7+1=f(c)23f(1)62f(1)+312f(1)9

Therefore, f(1)+f(0)20

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