AP EAMCET · Maths · Application of Derivatives
If the slope of the line through \((0,0)\) which is tangent to the curve \(y=x^2+x+16\) is \(m\) then the value of \(m-4\) is
- A \(9\)
- B \(10\)
- C \(12\)
- D \(13\)
Answer & Solution
Correct Answer
(A) \(9\)
Step-by-step Solution
Detailed explanation
\(y=x^2+x+16\) \(\left.\frac{d y}{d x}\right|_{(x 1, y 1)}=2 x_1+1\) \(\therefore\) Slope of line \(is\frac{y_1-0}{d_1-0}=\frac{y_1}{x_1}\) \(\therefore 2 x_1+1=\frac{y_1}{x_1}\) \(\Rightarrow 2 x_1^2+x_1=y_1\) ...(i) Also, \(\left(x_1, y_1\right.\) satisfies the curve:…
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