<h2>2.</h2><h3>Given</h3>
<h3>Find</h3>
- y·y'' +x·y' -16 in simplest form
<h3>Solution</h3>
It is convenient to expand the expression for y to ease determination of derivatives.
... y = 4x -6x²
... y' = 4 -12x
... y'' = -12
Then the differential expression can be written as
... (4x -6x²)(-12) +x(4 -12x) -16
... = -48x +72x² +4x -12x² -16
... = 60x² -44x -16
<h2>3.</h2><h3>Given</h3>
<h3>Find</h3>
- the turning points
- the extreme(s)
<h3>Solution</h3>
The derivative is
... y' = -16x^-2 + x^2
This is zero at the turning points, so
... -16/x^2 +x^2 = 0
... x^4 = 16 . . . . . . . . . multiply by x^2, add 16
... x^2 = ±√16 = ±4
We're only interested in the real values of x, so
... x = ±√4 = ±2 . . . . . . . x-values at the turning points
Then the turning points are
... y = 16/-2 +(-2)³/3 = -8 +-8/3 = -32/3 . . . . for x = -2
... y = 16/2 + 2³/3 = 8 +8/3 = 32/3 . . . . . . . for x = 2
The maximum is (-2, -10 2/3); the minimum is (2, 10 2/3).
The answer to your question will be 48.
Answer:
(-1,0)
Step-by-step explanation:
Convert the equation to vertex form which becomes y=(x+1)^2+0
Then we can see the vertex in the form (h,k) in y=a(x-h)^2+k
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Hope this helps!
<em>~ ShadowXReaper069</em></span>
You need to set both of them equal to zero to find what w is. so its 3w-5=0 you add 5 to get w by itself so then its 3w=5 and then divide by 3 so w= 5/3
1 + w = 0 so then you subtract one to get to the other side so w = -1
the final solution is {5/3, -1}
