Question

Any tangent to the curve y = 2x⁷ + 3x + 5 __________________ .

Options

• is parallel to x-axis

• is parallel to y-axis

• makes an acute angle with x-axis

• makes an obtuse angle with x-axis

Answer 1

makes an acute angle with x-axis

 

We have, y = 2x⁷ + 3x + 5

\[\frac{dy}{dx} = 14 x^6 + 3\]

\[ \Rightarrow \frac{dy}{dx} > 3 \left( \because x^6 \text { is always positive for any real value of } x \right)\]

\[ \Rightarrow \frac{dy}{dx} > 0\]

\[\text { So }, \tan\theta > 0\]

\[\text { Hence }, \theta \text { lies in first quadrant } . \]

\[\text { Thus, the tangent to the curve makes an acute angle with x - axis }\]