A function f is defined as follows, f(x) = * 20 c ,x & if , , ,x … - Vidyadip

MCQ

A function $f$ is defined as follows,

$f(x) =$ $\left\{ {\begin{array}{*{20}{c}} {\sin \,x}&{if\,\,\,x\,\, \leqslant \,\,c} \\ {ax\, + \,b}&{if\,\,\,x\,\, > \,\,c} \end{array}} \right.$ where $c$ is a known quantity.

If $f$ is derivable at $x = c$ , then the values of $'a'$ $and$ $'b’$ are _____ $and$______ respectively

A
$sin\, c \, and \,sin \,c - c \,cos\, c $
B
$sin\, c \, and \,sin \,c - c \,cos\, c $
C
$cos\, c \, and \,sin \,c+ c \,cos\, c $
✓
$cos\, c \, and \,sin \,c - c \,cos\, c $

✓

Answer

Correct option: D.

$cos\, c \, and \,sin \,c - c \,cos\, c $

d
. : $cos\, c \, \,and \,\,sin \,c - c \,cos\, c $

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