AP EAMCET · Maths · Application of Derivatives
The line joining the points \((0,3)\) and \((5,-2)\) is a tangent to the curve \(y=\frac{c}{x+1}\), then \(c=\)
- A \(1\)
- B \(-2\)
- C \(4\)
- D \(5\)
Answer & Solution
Correct Answer
(C) \(4\)
Step-by-step Solution
Detailed explanation
Slope of line joining the points \((0,3)\) and \((5,-2)\) is \(\frac{3+2}{0-5}=-1\) This is equal to the slope of tangent on the curve and that is given by \(\frac{d y}{d x}=\frac{-c}{(x+1)^2}\) \(\Rightarrow \quad \frac{d y}{d x}=-1\) \(\Rightarrow \quad c=(x+1)^2\) ...(i)…
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