JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(f\) and \(g\) are differentiable functions in \([0, 1]\) satisfying \(f\left( 0 \right) = 2 = g\left( 1 \right)\;,\;\;g\left( 0 \right) = 0,\) and \(f\left( 1 \right) = 6,\) then for some \(c \in \left] {0,1} \right[\) . .
- A \(f'\left( c \right) = g'\left( c \right)\)
- B \(f'\left( c \right) = 2g'\left( c \right)\)
- C \(2f'\left( c \right) = g'\left( c \right)\)
- D \(2f'\left( c \right) = 3g'\left( c \right)\)
Answer & Solution
Correct Answer
(B) \(f'\left( c \right) = 2g'\left( c \right)\)
Step-by-step Solution
Detailed explanation
\(2 g^{\prime}(c)=f^{\prime}(c)\) \(=2\left(\frac{g(1)-g(0)}{1-0}\right)=\left(\frac{f(1)-f(0)}{1-0}\right)\) \(=2\left(\frac{2-0}{1}\right)=\left(\frac{6-2}{1}\right) \Rightarrow 4=4\)
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