Let f'(x) be differentiable for allx. If f(1)=-2 andf'(x)≥2∀x∈1,6, then
f(6)<8
f(6)≥8
f(6)≥5
f(6)≤5
Explanation for the correct option:
f(1)=-2 andf'(x)≥2∀x∈1,6
f(x) be continuous on 1,6and differentiable on 1,6 , therefore, by Lagrange's mean value theorem:
∃c∈1,6 such that f'(c)=f(6)-f(1)6-1
f(6)-f(1)=5f'(c)≥10
f(6)+2≥10f(6)≥8
Hence, option (B) is the correct answer