Question

Given the function f(x) = 3/7 x^2 + 2x^3, find the value f(1/2) in simplest form.

Answer 1

Given

`f(x)=(3)/(7)x^2+2x^3`

You have to calculate f(1/2) to do so, replace the formula with x=1/2

`f((1)/(2))=(3)/(7)((1)/(2))^2+2((1)/(2))^3`

Following the order of operations, you have to solve the exponents first, then the multiplications and finally the addition.

1) Solve the exponents

`f((1)/(2))=(3)/(7)\cdot(1)/(4)+2\cdot(1)/(8)`

2) Solve the multiplications

`\begin{gathered} f((1)/(2))=(3)/(7)\cdot(1)/(4)+2\cdot(1)/(8) \\ f((1)/(2))=(3)/(28)+(1)/(4) \end{gathered}`

3) Solve the adition and simplify is necessary

`\begin{gathered} f((1)/(2))=(3)/(28)+(1)/(4)=(3+7)/(28) \\ f((1)/(2))=(10)/(28)=(5)/(14) \end{gathered}`