WBJEE · Maths · Application of Derivatives
Let \(f\) be a function which is differentiable for all real \(x\). If \(f(2)=-4\) and \(f^{\prime}(x) \geq 6\) for all \(x \in[2,4]\)
- A \(f(4) \lt 8\)
- B \(f(4) \geq 12\)
- C \(f(4) \geq 8\)
- D \(f(4) \lt 12\)
Answer & Solution
Correct Answer
(C) \(f(4) \geq 8\)
Step-by-step Solution
Detailed explanation
By LMVT \(f^{\prime}(x)=\frac{f(4)-f(2)}{4-2}\) as \(f^{\prime}(x) \geq 6 \Rightarrow f(4) \geq 8\)
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