Ben owns a townhome valued at $ 195,000, but still owes $120,000 on the loan. ben has $5,000 in savings and balance of $1,400 on his credit cards. there is a balance of $20,000 owed on ben's car which is valued at $ 38,000. what is ben's net worth?

Net worth is the difference between assets and liabilities.

Assets - liabilities = net worth

Assets include
townhome valued at $ 195,000
savings 5000
Car 38000
Total=195,000+5,000+38,000
=238,000

Liabilities include
Loan owed 120000
Credit card 1400
owed on Ben's car 20000
Total=120,000+1,400+20,000
=141,400

Net worth=238,000−141,400=96,600

Compute the derivative:



Set equal to zero and find the critical points:



Compute the second derivative at the critical points to determine concavity. If the second derivative is positive, the function is concave upward at that point, so the function attains a minimum at the critical point. If negative, the critical point is the site of a maximum.



At , the second derivative takes on the value of , so the function is concave upward, so the function has a minimum there of .

At , the second derivative is , so the function is concave downward and has a maximum there of .