Define the piecewise function where is a real parameter

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

Problem

Define the piecewise function

s_\lambda(x)=\begin{cases}x^2+\lambda x,&0\le x\le 2,\\4x-\lambda,&2< x\le 5,\end{cases}

where

\lambda

is a real parameter. For which values of

\lambda

does

s_\lambda

attain its absolute maximum on

[0,5]

x=5

? (a)

\lambda\ge \dfrac{16}{3}

(b)

-4\le \lambda\le \dfrac{16}{3}

(c)

\lambda\le \dfrac{16}{3}

(d)

\lambda\le \dfrac{20}{3}