# (Solved): QUESTION 3 3.1.1 Determine the coordinates of the turning points of: f(x)=x^(3)+3x^(2)-2 3.1.2 Draw ...

QUESTION 3 3.1.1 Determine the coordinates of the turning points of:

`f(x)=x^(3)+3x^(2)-2`

3.1.2 Draw up a table of values of

`x`

and

`f(x)`

for the values of

`x`

from -3 to 1 and make a neat sketch of this part of the curve. 3.1.3 Use the table and the sketch to estimate a value of the negative root of

`x^(3)+3x^(2)-2=0`

and then use Newton's/ Taylor's method to determine a better approximation of this root correct to THREE decimal figures. Use ONE approximation. (5) 3.2 A body moves along a straight line according to the law

`s=t^(3)-t^(2)+6t+2`

where

`s=`

distance covered in metres, and

`t=`

time in seconds. Calculate: 3.2.1 The velocity after 1 second. (3) 3.2.2 The acceleration after 1 second. 3.3 The circumference of a circle is increasing at a rate of

`2c(m)/(s)`

. Fin the rate of increase of area when the radius is

`4cm`

.

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