
has critical points wherever the partial derivatives vanish:


Then

- If
, then
; critical point at (0, 0) - If
, then
; critical point at (1, 1) - If
, then
; critical point at (-1, -1)
has Hessian matrix

with determinant

- At (0, 0), the Hessian determinant is -16, which indicates a saddle point.
- At (1, 1), the determinant is 128, and
, which indicates a local minimum. - At (-1, -1), the determinant is again 128, and
, which indicates another local minimum.
It is d Ik Bc Ik don’t ask why just know it’s d
V = a ^ 3
V= 5 ^ 3 = 125 cm cube
-|2x+3| > 2 and <span>-|2x+3| > - 2
</span>-2x+3 > 2
-2x > 2 - 3
-2x > -1
-2x / -2 > -1 / -2
x < 1/ 2
-|2x+3| > - 2
x < 5/2
Answers:measure angle x = 40°
measure angle y = 35°
measure angle z = 55°
Explanation:Part (a): getting angle x:In triangle BED, we have:
measure angle BED = 90°
measure angle BDE = 50°
Therefore:
measure angle DBE = 180 - (90+50) = 40°
Now, we have angle DBE and angle GBF vertically opposite angles.
This means that they are both equal. Therefore angle GBF = 40°
Since angle GBF is x, therefore:
x = 40°
Part (b): getting angle y:We know that the sum of measures of angles on a straight line is 180.
This means that:
angle GBF + angle GBC + angle CBE = 180
We have:
angle GBF = 40°
angle GBC = 105°
angle CBE = y
Therefore:
40 + 105 + y = 180
y = 35°
Part (c): getting angle z:In triangle BCE, we have:
measure angle BCE = z
measure angle BEC = 90°
measure angle CBE = 35°
Therefore:
z + 90 + 35 = 180
z = 55°
Hope this helps :)