AP EAMCET · Maths · Application of Derivatives
If the tangent drawn to the curve \(\mathrm{y}=\mathrm{x}^3\) at a point \((\alpha, \beta)\) cuts again the curve at another point \(\left(\alpha_1, \beta_1\right)\), then \(\frac{\beta_1}{\beta}=\)
- A -2
- B 1
- C -8
- D 27
Answer & Solution
Correct Answer
(C) -8
Step-by-step Solution
Detailed explanation
\(\because y=x^3\) Equation of tangent line at point \((\alpha, \beta)\) is: \((y-\beta)=3 \alpha^2(x-\alpha)\) \(\because\left(\alpha_1, \beta_1\right)\) lies on equation (i), we get \(\beta_1-\beta=3 \alpha^2\left(\alpha_1-\alpha\right)\)…
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