JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f\) be a twice differentiable function on \((1,6) .\) If \(f (2)=8, f ^{\prime}(2)=5, f ^{\prime}( x ) \geq 1\) and \(f ^{\prime \prime}( x ) \geq 4,\) for all \(x \in(1,6),\) then
- A \(f(5) \leq 10\)
- B \(f^{\prime}(5)+f^{\prime \prime}(5) \leq 20\)
- C \(f(5)+f^{\prime}(5) \geq 28\)
- D \(f(5)+f^{\prime}(5) \leq 26\)
Answer & Solution
Correct Answer
(C) \(f(5)+f^{\prime}(5) \geq 28\)
Step-by-step Solution
Detailed explanation
\(f(2)=8, f^{\prime}(2)=5, f^{\prime}(x) \geq 1, f^{\prime \prime}(x) \geq 4, \forall x \in(1,6)\) \(f ^{\prime \prime}( x )=\frac{ f ^{\prime}(5)- f ^{\prime}(2)}{5-2} \geq 4 \Rightarrow f ^{\prime}(5) \geq 17\)…
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