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.
First find the total payments
Total paid
200×30=6,000 (this is the future value)
Second use the formula of the future value of annuity ordinary to find the monthly payment.
The formula is
Fv=pmt [(1+r/k)^(n)-1)÷(r/k)]
We need to solve for pmt
PMT=Fv÷[(1+r/k)^(n)-1)÷(r/k)]
PMT monthly payment?
Fv future value 6000
R interest rate 0.09
K compounded monthly 12
N=kt=12×(30months/12months)=30
PMT=6000÷(((1+0.09÷12)^(30)
−1)÷(0.09÷12))
=179.09 (this is the monthly payment)
Now use the formula of the present value of annuity ordinary to find the amount of his loan.
The formula is
Pv=pmt [(1-(1+r/k)^(-n))÷(r/k)]
Pv present value or the amount of his loan?
PMT monthly payment 179.09
R interest rate 0.09
N 30
K compounded monthly 12
Pv=179.09×((1−(1+0.09÷12)^(
−30))÷(0.09÷12))
=4,795.15
The answer is 4795.15
Answer:
x> 3/20
Step-by-step explanation:
Let's solve your inequality step-by-step.
1
/5 + 1
/3 x> 1
/2 − 1
/4
Step 1: Simplify both sides of the inequality.
1
/3
x+ 1
/5 > 1
/4
Step 2: Subtract 1/5 from both sides.
1
/3
x+ 1/
5 − 1
/5 > 1
/4 − 1
/5 1
/3 x> 1
/20
Step 3: Multiply both sides by 3.
3*(
1
/3
x)>3*(
1
/20
)
x>
3
/20
Answer:
x> 3/
20
Hope this helps!!
Sure What do u need help with I am always here