Let be the function defined by g(x)= cases x^ 2 -4x+5, & x<3, 9-2x, & x 3

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Let

g

be the function defined by

g(x)= \begin{cases} x^{2}-4x+5, & x<3,\\ 9-2x, & x\ge 3. \end{cases}

Which description correctly classifies the behavior of

g

x=3

? (a) Neither a maximum nor a minimum because

g'(x)

is not defined at

x=3

. (b) Relative maximum because

g'(x)

changes from positive to negative at

x=3

. (c) Relative minimum because

g'(x)

changes from negative to positive at

x=3

. (d) Relative minimum because

g'(3)=0