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Tangents and Normals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSTangents and Normals1 Mark
MCQ
Any tangent to the curve $y = 2x^7 + 3x + 5:$
  • A
    Is parallel to $x-$axis.
  • B
    Is parallel to $y-$axis.
  • ✓
    Makes an acute angle with $x-$axis.
  • D
    Makes an obtuse angle with $x-$axis.
✓

Answer

Correct option: C.
Makes an acute angle with $x-$axis.
We have, $y = 2x^7 + 3x + 5$
$\frac{\text{dy}}{\text{dx}}=14\text{x}^6+3$
$\Rightarrow\frac{\text{dy}}{\text{dx}}>3 (\because x^{6 }$ is always positive for any real value of $x)$
$\Rightarrow\frac{\text{dy}}{\text{dx}}>0$
So, $\tan\theta > 0$
Hence, $\theta$ lies in first quadrant.
Thus, the tangent to the curve makes an acute angle with $x-$axis.

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