Question

Assertion :Any tangent to the curve $y=x^7+8x^3+2x+1$ makes an acute angle with the positive x - axis Reason: Any tangent to the curve $y=a_0{x}^{2n-1}+a_1{x}^{2n-1}+a_2{x}^{2n-3}+.......a_{n}x+1$ makes an acute angle with the positive x - axis where $a_1,........a_{n-1}\ge 0;a_0>0$ and $n\in N$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Given, $y=x^7+8x^3+2x+1$

$\therefore \frac{dy}{dx}=7x^6+24x^2+2$

which is always positive.

Thus any tangent to the given curve will make acute angle with the +ve x-axis.
Hence Assertion is correct.

Also, the derivative of $y$ in the reason is always positive. Thus reason is also correct and Assertion is followed by Reason.