Consider the function f(x)= cases x^2-4 x-2 , & x<2
MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
Consider the function
f(x)=⎩⎨⎧x−2x2−4,mx+n,x<2,x≥2.
where m and n are real constants.
(1) Part 1: (a) Determine the limit of f(x) as x approaches 2 from the left.
(2) Part 2: (b) Determine the limit of f(x) as x approaches 2 from the right in terms of m and n.
(3) Part 3: (c) Find all values of m and n that make f continuous on the entire real line.
(4) Part 4: (d) State every maximal open interval on which the resulting continuous function is differentiable and justify your answer.