Question about using $y''$ to determinenature of stat points

Can you use $y''$ to determine the nature of stationary points?  YES

• If $y''<0$ for some stat point then it is a MAX (Concave down).
• If $y''>0$ for some stat point then it is a MIN (Concave up).
• If $y''=0$ for some stat point then you MUST use the first derivative test box to see what it is :-)

EXAMPLE: $y=x^2-1$

$y'=2x$  stationary point is when $x=0$

Here, $y''=2>0$.

$(0,-1)$ is the stat point.

Since $y''(0)=2$ , so $y''>0$ and hence its a MIN.

You can verify this with the first derivative test.

JH :-)

Grove Prelim Book 2U 11.7 Question 1

$y=x^2/12$

$y'=x/6$

At x=6, $y'=6/6=1$

Normal gradient is $m=-1/1=-1$

$y-3=-1(x-6)$

$y-3=-x+6$

$y=-x+9$

Solve 
$y=-x+9$  (1)
$x^2=12y$   (2)

(1) x 12:
$12y=-12x+108$   (1)

so (1) subbed into (2) gives

$x^2=-12x+108$

$x^2+12x-108=0$                  

                  sandbox:  108=54 x 2 = 27 x 2^2 = 3^3 x 2^2
                                                                           3x2=6, 3^2 x 2=18!! yes

$(x+18)(x-6)=0$

$x=-18$ is where the normal cuts the parabola again.

$y=- -18 +9=27$

$P(-18,27)$

Primitive fn question

Grove 2U HSC EX5.3 Q10 A sector of a circle with radius 5cm and angle pie/3 subtended at the centre is cut out of card board. It is then curved around to make a cone. Find Exact SA and V.

Grove 2U HSC EX5.3 Q10 

A sector of a circle with radius 5cm and angle pie/3 subtended at the centre is cut out of card board. It is then curved around to make a cone. Find Exact SA and V.