Determine the linearization of the given function at the specified value of x. f ( x ) = 3 2 + x + 4 − x − 5 f\left(x\right)=\frac{3}{2+x}+\sqrt{4-x}-5 at x = 0 x=0

L ( x ) = − 3 2 − x L\left(x\right)=-\frac32-x

L ( x ) = 4 3 + x L\left(x\right)=\frac43+x

L ( x ) = 3 x − 2 x 2 L\left(x\right)=3x-2x^2

L ( x ) = x + 3 L\left(x\right)=\sqrt{x+3}

5. Applications of Derivatives

5. Applications of Derivatives / Linearization / Problem 8

Problem 8

Determine the linearization of the given function at the specified value of x.
$f (x) = \frac{3}{2 + x} + \sqrt{4 - x} - 5$ at $x equals 0$

$L (x) = \frac{4}{3} + x$

$L (x) = 3 x - 2 x^{2}$

$L (x) = - \frac{3}{2} - x$

$L (x) = \sqrt{x + 3}$