For the family of functions defined on the interval

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

For the family of functions

F_a(x)=x^{3}-2a x+a

defined on the interval

[0,2]

, determine all real numbers

a

for which the equation

F_a(x)=0

has at least one solution in

[0,2]

. State your reasoning clearly.