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
.