Any tangent to the curve y = 3x⁷ + 5x + 3 :

Any tangent to the curve $y = 3x^7 + 5x + 3$ :

(a)is parallel to x – axis
(b)is parallel to y – axis
(c)makes an acute angle with x – axis
(d)makes on obtuse angle with y – axis

Answer

Correct option: (c)

Answer: (c) makes an acute angle with x – axis $\frac{dy}{dx}=21x^6+5\ge5>0$ for all $x$, so the slope of every tangent is positive. Hence every tangent makes an acute angle with the x-axis.