WBJEE · Maths · Application of Derivatives
Let \(f:[1,3] \rightarrow \mathbb{R}\) be continuous and be derivable in \((1,3)\) and \(f^{\prime}(x)=[f(x)]^2+4 \forall x \in(1,3)\). Then
- A \(f(3)-f(1)=5\) holds
- B \(f(3)-f(1)=5\) does not hold
- C \(f(3)-f(1)=3\) holds
- D \(f(3)-f(1)=4\) holds
Answer & Solution
Correct Answer
(B) \(f(3)-f(1)=5\) does not hold
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Hint : } f^{\prime}(c)=(f(c))^2+4=\frac{f(3)-f(1)}{2} \\ & \Rightarrow f(3)-f(1)=2(f(c))^2+8 \end{aligned}\)
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