TS EAMCET · Maths · Application of Derivatives
The maximum interval in which the slopes of the tangents drawn to the curve \(y=x^4+5 x^3+9 x^2+6 x+2\) increase is
- A \(\left[\frac{-3}{2},-1\right]\)
- B \(\left[1, \frac{3}{2}\right]\)
- C \(R-\left[1, \frac{3}{2}\right]\)
- D \(R-\left[\frac{-3}{2},-1\right]\)
Answer & Solution
Correct Answer
(D) \(R-\left[\frac{-3}{2},-1\right]\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & y=x^4+5 x^3+9 x^2+6 x+2 \\ & \text {Slope of tangents }=\frac{d y}{d x}=4 x^3+15 x^2+18 x+6 \\ & \frac{d^2 y}{d x^2}=12 x^2+30 x+18=12\left(x+\frac{3}{2}\right)(x+1)\end{aligned}\) \(\therefore \frac{d y}{d x}\) is increasing in \({R}-[-\frac{3}{2},-1]\)
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