By definition of absolute value, you have
or more simply,
On their own, each piece is differentiable over their respective domains, except at the point where they split off.
For <em>x</em> > -1, we have
(<em>x</em> + 1)<em>'</em> = 1
while for <em>x</em> < -1,
(-<em>x</em> - 1)<em>'</em> = -1
More concisely,
Note the strict inequalities in the definition of <em>f '(x)</em>.
In order for <em>f(x)</em> to be differentiable at <em>x</em> = -1, the derivative <em>f '(x)</em> must be continuous at <em>x</em> = -1. But this is not the case, because the limits from either side of <em>x</em> = -1 for the derivative do not match:
All this to say that <em>f(x)</em> is differentiable everywhere on its domain, <em>except</em> at the point <em>x</em> = -1.
Answer: Bottom and top (or which ever one is the small box in the middle and the one that looks like the small box in the middle)
Step-by-step explanation: the middle rectangle is the bottom and the other one like it is the top. the length is 7 in. and the height is 4 in. and 4 in. times 7 in. is 28in^2
Assume:
Size of sides = x m
Depth of the pool = y m
Therefore, surface area = x^2+4xy =10 m^2
Then, y = (10-x^2)/(4x)
Now,
Volume (V) = x^2*y = x^2*y =x^2(10-x^2)/4x = (10x-x^3)/4 = 1/4(10x-x^3)
For maximum volume, first derivative of volume function is equal to zero.
That is,
dV/dx =0 = 1/4(10-3x^2)
Then,
1/4(10-3x^2) = 0
10-3x^2 = 0
3x^2=10
x= sqrt (10/3) = 1.826 m
And
y= (10-1.826^2)/(4*1.826) = 0.913 m
Therefore,
V= 1.826^2*0.913 = 3.044 m^3
A.) 5/162
the numerator is increasing by 1 and the denominator is being multiplied by 3 each time
Hello!
<h2>Answer: </h2>
23. 138 people voted for Nyemi, 69 people voted for Luke, and 23 people voted for Natalie.
24. Reina did not ride 11/16 of the rides.
<h2>
Explanation:</h2>
23:
3 ÷ 5 = 0.6
230 × 0.6 = 138
230 × 0.3 = 69
230 × 0.1 = 23
24:
We know that Alberto rode 5/8 of the rides at the park, and Reina rode half of this.
5/8 × 1/2 = 5/16
16 - 5 = 11
