AP EAMCET · Maths · Application of Derivatives
If the tangent drawn to the curve \(y=x^3-a x^2+x+1\) at each point \(x \in \mathbb{R}\), is inclined at an acute angle with the positive direction of \(\mathrm{X}\) - axis, then the set of all possible values of ' \(a\) ' is
- A \(\mathbb{R}-(-\sqrt{3}, \sqrt{3})\)
- B \([-3,3]\)
- C \(\mathbb{R}\)
- D \((-\sqrt{3}, \sqrt{3})\)
Answer & Solution
Correct Answer
(D) \((-\sqrt{3}, \sqrt{3})\)
Step-by-step Solution
Detailed explanation
Given \(y=x^3-a x^2+x+1\) \[ \Rightarrow \frac{d y}{d x}=3 x^2-2 a x+1 \] Since \(\theta\) is an acute angle. Hence \(\tan \theta>0\) \[ \Rightarrow 3 x^2-2 a x+1>0 \] Which is true off \(A>0\) and…
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