Answer:
a) d²y/dx² = ½ x + y − ½
b) Relative minimum
Step-by-step explanation:
a) Take the derivative with respect to x.
dy/dx = ½ x + y − 1
d²y/dx² = ½ + dy/dx
d²y/dx² = ½ + (½ x + y − 1)
d²y/dx² = ½ x + y − ½
b) At (0, 1), the first and second derivatives are:
dy/dx = ½ (0) + (1) − 1
dy/dx = 0
d²y/dx² = ½ (0) + (1) − ½
d²y/dx² = ½
The first derivative is 0, and the second derivative is positive (concave up). Therefore, the point is a relative minimum.
7. E
8.C
9. F
10.D
11.B
12.A
13.G
I think this is right
Number 16 is 13.5 because each half triangle is 1 unif square
Y - 2 = -3/4 (x - 6)
y = -3/4 (x - 6) + 2
When, x = -2,
y = -3/4 (-2 - 6) + 2 = -3/4 (-8) + 2 = 6 + 2 = 8
One point is (-2, 8)
When, x = 2,
y = -3/4 (2 - 6) + 2 = -3/4 (-4) + 2 = 3 + 2 = 5
Another point is (2, 5)
