For the cubic function f(x)=x^ 3 -3kx

MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

For the cubic function

f(x)=x^{3}-3kx,

answer the following: (i) Obtain the critical points of

f

in terms of

k

. (ii) Determine the values of

k

for which the curve

y=f(x)

has a local maximum at

x=-1