Randall and augustine are financing $148,000 to purchase a condo. they obtained a 15 year fixed rate loan with a rate of 4.95%. they have vern given the option of purchasing up to five points to lower their rate to 4.73%. how much will the five points cost them?

a - $7,000.40
b - $325.60
c - $1,480.00
d - $7,400.00

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Ответ:

tyw3366812778

22.06.2021

Mathematics

$\frac{df(x)}{dx}=20x\\$

Step-by-step explanation:

to find the derivative of the function $f(x)=10x^{2}$ we use the chain rule approach. which simply involves increasing x by Δx and carrying out simple arithmetic operation.

The First step is to increase x by Δx

$f(x)=10x^{2} \\$

increase x by Δx and and f(x) by Δf(x)

$f(x) +Δf(x)=10(x+Δx)^{2} \\$

if we expand we have

$f(x) +Δf(x)=10(x^{2}+2xΔx+(Δx)^{2})\\$

if we expand we have

$f(x) +Δf(x)=10x^{2}+20xΔx+10(Δx)^{2}\\$

next we subtract f(x) from both sides

$f(x) +Δf(x)-f(x)=10x^{2}+20xΔx+10(Δx)^{2}-f(x)\\$

$Δf(x)=10x^{2}+20xΔx+10(Δx)^{2}-10x^{2}\\$

$Δf(x)=20xΔx+10(Δx)^{2}\\$

Next we divide all through by Δx

$Δf(x)/Δx=20xΔx/Δx+10(Δx)^{2}/Δx\\$

$Δf(x)/Δx=20x+10Δx\\$

next we let the limit of Δx tends zero, we arrive at

$\frac{df(x)}{dx}=20x\\$

hence the derivative of the function $f(x)=10x^{2} \\$ is $\frac{df(x)}{dx}=20x\\$

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