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Q.

Let f be a twice differentiable function on (1,6) . If f(2)=8,f'(2)=5,f'(x)≥1 andf "(x)≥4 , for  all x∈(1,6) , then :

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a

f5≤10

b

f'5+f"5≤20

c

f5+f'5≤26

d

f5+f'5≥28

answer is D.

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Detailed Solution

f'(x)≥1⇒∫25f'(x)dx≥∫25dxf(5)-f(2)≥3    f(5)≥11 Also f''(x)≥4⇒∫25f''(x)dx≥∫254dxf'(5)-f'(2)≥12f'(5)≥17⇒f(5)+f'(5)≥28
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