Q43 / 155 · WBJEE 2023 · Mathematics

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
  • Correct answer
    B
    \(f(3)-f(1)=5\) does not hold
  • C
    \(f(3)-f(1)=3\) holds
  • D
    \(f(3)-f(1)=4\) holds

Solution

\(\begin{aligned} & \text { Hint : } f^{\prime}(c)=(f(c))^2+4=\frac{f(3)-f(1)}{2} \\ & \Rightarrow f(3)-f(1)=2(f(c))^2+8 \end{aligned}\)

Hence, the correct answer is option: 'B'.

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