JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(f(x)\) and \(g(x)\) be twice differentiable functions satisfying \(f''(x) = g''(x)\) for all \(x \in \mathbf{R}\), \(f'(1) = 2g'(1) = 4\) and \(g(2) = 3f(2) = 9\). Then \(f(25) - g(25)\) is equal to :
- A \(20\)
- B \(40\)
- C \(-20\)
- D \(-40\)
Answer & Solution
Correct Answer
(B) \(40\)
Step-by-step Solution
Detailed explanation
Given \(f''(x) = g''(x)\) for all \(x \in \mathbf{R}\). Let \(h(x) = f(x) - g(x)\). Taking the second derivative, \(h''(x) = f''(x) - g''(x) = 0\). Integrating with respect to \(x\), \(h'(x) = c_1\). Given \(f'(1) = 4\) and \(g'(1) = 2\), \(h'(1) = f'(1) - g'(1) = 4 - 2 = 2\).…
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