Answer:
One order pair is
(
2,0)
Step-by-step explanation:
What ordered pairs are the options?
Pick a value for
x
and solve for
y
. Or find the intercepts.
If
x
=
2
, then:
y
=
2
−
2
⇒
y
=
0
So we have
(
2
,
0
)
If
x
=
0
, then:
y
=
0
−
2
⇒
y
=
−
2
Here we have
(
0
,
−
2
)
You can simply use
0
for both
x
and
y
(intercept) to get the same answer.
<span>, y+2 = (x^2/2) - 2sin(y)
so we are taking the derivative y in respect to x so we have
dy/dx use chain rule on y
so y' = 2x/2 - 2cos(y)*y'
</span><span>Now rearrange it to solve for y'
y' = 2x/2 - 2cos(y)*y'
0 = x - 2cos(y)y' - y'
- x = 2cos(y)y' - y'
-x = y'(2cos(y) - 1)
-x/(2cos(y) - 1) = y'
</span><span>we know when f(2) = 0 so thus y = 0
so when
f'(2) = -2/(2cos(0)-1)
</span><span>2/2 = 1
</span><span>f'(2) = -2/(2cos(0)-1)
cos(0) = 1
thus
f'(2) = -2/(2(1)-1)
= -2/-1
= 2
f'(2) = 2
</span>
The answer for this question is 8/1
