The function is defined for all real

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

The function

f(x)=\dfrac{x^{3}-3x}{x^{2}+1}

is defined for all real

x

. Which ordered pair best represents the number of horizontal tangents (first entry) and vertical tangents (second entry) of the graph of

f

? (a)

(1,0)

(b)

(2,1)

(c)

(2,0)

(d)

(0,0)