TS EAMCET · Maths · Application of Derivatives
\(x_1, x_2 \in \mathbf{N}\). If a line having slope 2 is a tangent to the curve \(y=x^4-6 x^3+13 x^2-10 x+5\) at points \(P\left(x_1, y_1\right)\) and \(Q\left(x_2, y_2\right)\), then \(x_1 x_2+y_1 y_2=\)
- A 17
- B -5
- C 13
- D -10
Answer & Solution
Correct Answer
(A) 17
Step-by-step Solution
Detailed explanation
Equation of given curve is \(y=x^4-6 x^3+13 x^2-10 x+5\) So, \(\quad \frac{d y}{d x}=4 x^3-18 x^2+26 x-10\) As the slope of tangent at point \(P\left(x_1, y_1\right)\) and \(Q\left(x_2, y_2\right)\) on curve is given as 2 , so put \(\frac{d y}{d x}=2\)…
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