Continuous differentiable f satisfies f ( 2 ) = − 4 and f ′ ( x ) ≥ 6 on [2, 4]. Then

By the mean value theorem, [ f ( 4 ) − f ( 2 )] /2 = f ′ ( c ) ≥ 6 . Hence f ( 4 ) + 4 ≥ 12 , so f ( 4 ) ≥ 8 .

Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-LMVTEasy2 minQB

MathematicsEasysingle choice

Continuous differentiable $f$ satisfies $f (2) = - 4$ and $f_{'} (x) \geq 6$ on [2, 4]. Then

Answer:

Solution:

By the mean value theorem, $[f (4) - f (2)] /2 = f' (c) \geq 6$ . Hence $f (4) + 4 \geq 12$ , so $f (4) \geq 8$ .

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Monotonicity-LMVT

⏱ 2mℹ️ Source: QB

Loading discussions...