Let then which of the following is (are) correct.

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

f(x)=\frac{x^3-4}{(x-1)^3}

then which of the following is (are) correct. (a)

\lim_{x\to-\infty} f(x)=-1

(b)

x=-2

is the point of local minimum. (c) The equation

f(x)=c

will have three real and distinct roots for

c\in(\frac{4}{9},1)\cup(1,4)

. (d) The line

y=1

intersects the graph of

f(x)

at exactly one point.