Select correct option(s) with regards to tangent/normal drawn at any point on the curve $y=x^5+8x+1$.

(A) Tangent makes acute angle with x-axis
(B) Normal makes acute angle with x-axis
(C) Tangent makes obtuse angle with x-axis
(D) Normal makes obtuse angle with x-axis
(E) None of the options above as the angle made by tangent/normal with x-axis being acute/obtuse depends on the point chosen

Solution

Slope of tangent at any point $m=\frac {dy}{dx} = 5x^4+8$

Clearly m > 0

So, the tangent makes acute angle with x-axis.

Thus, the normal makes obtuse angle with x-axis.

Hence, (A) & (D)