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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-Increasing-DecreasingMedium2 minQB

MathematicsMediumsingle choice

If at each point of the curve $y = x^{3} - a x^{2} + x + 1$ the tangent is inclined at an acute angle with the positive direction of the x-axis, then a lies in the interval [0pt]

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Answer:

Solution:

$\frac{d y}{d x} = 3 x^{2} - 2 a x + 1, \frac{d y}{d x} > 0 \Rightarrow 3 x^{2} - 2 a x + 1 > 0$ for all $x$ ⇒ discriminant $4 a^{2} - 12 < 0 \Rightarrow a \in (- 3, 3)$

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Monotonicity-Increasing-Decreasing

⏱ 2mℹ️ Source: QB

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