AP EAMCET · Maths · Differentiation
If \(f(x)\) is differentiable on \(\mathbb{R}, f(x) f^{\prime}(-x)-f(-x) f^{\prime}(x)=0\), \(f(x) f^{\prime}(-x)=0, f(0)=3\) and \(f(3)=9\), then \((1+f(-3))^3+1=\)
- A \(2\)
- B \(9\)
- C \(28\)
- D \(0\)
Answer & Solution
Correct Answer
(B) \(9\)
Step-by-step Solution
Detailed explanation
Given, \(f(x) f^{\prime}(-x)-f(-x) f^{\prime}(x)=0\) \[ \Rightarrow f(-x) f^{\prime}(x)-f^{\prime}(-x) f(x)=0 \] \[ \Rightarrow \frac{d}{d x}[f(-x) f(x)]=0 \] \(\Rightarrow f(-x) \cdot f(x)=c\) where \(c=\) Arbitrary constant when \(x=0\), then…
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