question:

Find the linear approximation,L(x),

off(x) =

x

atx=4.

L(x) =

Use the linear approximation to approximate

4.3

.

L(4.3) =

and

Use Newton's method to approximate the positive root ofx³+3x5= 0

to three consistent decimal places.

and

Use Newton's method to approximate all real roots ofx⁴x1= 0

to three consistent decimal places. (Enter your answers as a comma-separated list.)

x=

and

Find the global minimum and maximum of the continuous functionf(x) =x²8 ln(x)

on[1,4].

(Round your answers to two decimal places.)

global minimum value_______

global maximum value________