Algebra 1 rate of change
Introduction :
Algebra 1 rate of change involves the process of finding rate of change in the algebraic equations with detailed solutions. In calculus, rate of change is calculated with the help of differential calculus and integral calculus. Generally the main function of the calculus is to find the rate of change of the given algebraic function with respect to change in the input function. The following are the solved example problems in algebra 1 to find the rate of change.
Algebra 1 rate of change example problems:
Example 1:
Solve the algebra 1 equation to find rate of change.
f(b) = 2b 2 – 4 b 4 + 8b
Solution:
The given function is
f(b) = 2b 2 – 4b 4 + 8b
Differentiate the math function
f '(b) = 2(2b ) – 4(4b 3 ) + 8
Solving the above terms we get,
f '(b) = 4b – 16b 3 + 8 is the answer.
Example 2:
Solve the algebra 1 equation to find rate of change.
`int ` f(b) = 2b+3b2+4 b3 + 5 b4 db
Solution:
The given function is
`int ` f(b) = 2b+3b2+4 b3 + 5 b4 db
`int ` f(b) = `int ` (2b+3b2+ 4b3 + 5 b4) db
`int ` f(b) = `int ` 2b db + `int ` 3b2 db+ `int ` 4 b3 db + `int ` 5 b4 db
Integrate the math function.
We get
`F(b) = (2b^2)/2 + (3b^3)/3 + (4 b^4)/4 + (5b^5)/5`
Solving the above function we get
F(b) = b2+ b3 +b4 + b5 is the answer.
Example 3:
Solve the algebra 1 equation to find rate of change.
f(b) = 3b4 – 6b 5 – 9 b 6 + 12
Solution:
The given function is
f(b) = 3b4 – 6b 5 – 9 b 6 + 12
Differentiate the math function
f '(b) = 3(4 b3) – 6(5b 4 ) – 9( 6b 5)
Solving the above terms we get,
f '(b) = 12 b3 – 30b 5 – 54b 5 is the answer.
Example 4:
Solve the algebra 1 equation to find rate of change..
`int ` f(b) = 18b5+20b4+4b db
Solution:
The given function is
`int ` f(b) = 18b5+20b4+4b db
`int ` f(b) = `int ` (18b5+20b4+4b) db
`int ` f(b) = `int ` 18b5 db + `int ` 20b4 db + `int ` 4b db
Integrate the math function.
We get
`F(b) = (18b^6)/6 + (20b^5)/5 + (4b^2) /2`
Solving the above function we get
F(b) =3b6+ 4b5 +2b2 is the answer.
Algebra 1 rate of change practice problems:
1) Solve the algebra 1 equation to find rate of change.
f(b) = 4b 3 – 5b + 16
Answer: f '(b) = 12b 2 – 5
2) Solve the algebra 1 equation to find rate of change.
`int ` f(b) = 2b2+6b db
Answer:` F(b) = (2b^3)/3 + 3b^2`
Algebra 1 rate of change involves the process of finding rate of change in the algebraic equations with detailed solutions. In calculus, rate of change is calculated with the help of differential calculus and integral calculus. Generally the main function of the calculus is to find the rate of change of the given algebraic function with respect to change in the input function. The following are the solved example problems in algebra 1 to find the rate of change.
Algebra 1 rate of change example problems:
Example 1:
Solve the algebra 1 equation to find rate of change.
f(b) = 2b 2 – 4 b 4 + 8b
Solution:
The given function is
f(b) = 2b 2 – 4b 4 + 8b
Differentiate the math function
f '(b) = 2(2b ) – 4(4b 3 ) + 8
Solving the above terms we get,
f '(b) = 4b – 16b 3 + 8 is the answer.
Example 2:
Solve the algebra 1 equation to find rate of change.
`int ` f(b) = 2b+3b2+4 b3 + 5 b4 db
Solution:
The given function is
`int ` f(b) = 2b+3b2+4 b3 + 5 b4 db
`int ` f(b) = `int ` (2b+3b2+ 4b3 + 5 b4) db
`int ` f(b) = `int ` 2b db + `int ` 3b2 db+ `int ` 4 b3 db + `int ` 5 b4 db
Integrate the math function.
We get
`F(b) = (2b^2)/2 + (3b^3)/3 + (4 b^4)/4 + (5b^5)/5`
Solving the above function we get
F(b) = b2+ b3 +b4 + b5 is the answer.
Example 3:
Solve the algebra 1 equation to find rate of change.
f(b) = 3b4 – 6b 5 – 9 b 6 + 12
Solution:
The given function is
f(b) = 3b4 – 6b 5 – 9 b 6 + 12
Differentiate the math function
f '(b) = 3(4 b3) – 6(5b 4 ) – 9( 6b 5)
Solving the above terms we get,
f '(b) = 12 b3 – 30b 5 – 54b 5 is the answer.
Example 4:
Solve the algebra 1 equation to find rate of change..
`int ` f(b) = 18b5+20b4+4b db
Solution:
The given function is
`int ` f(b) = 18b5+20b4+4b db
`int ` f(b) = `int ` (18b5+20b4+4b) db
`int ` f(b) = `int ` 18b5 db + `int ` 20b4 db + `int ` 4b db
Integrate the math function.
We get
`F(b) = (18b^6)/6 + (20b^5)/5 + (4b^2) /2`
Solving the above function we get
F(b) =3b6+ 4b5 +2b2 is the answer.
Algebra 1 rate of change practice problems:
1) Solve the algebra 1 equation to find rate of change.
f(b) = 4b 3 – 5b + 16
Answer: f '(b) = 12b 2 – 5
2) Solve the algebra 1 equation to find rate of change.
`int ` f(b) = 2b2+6b db
Answer:` F(b) = (2b^3)/3 + 3b^2`