Question

I need help question number 5

Answer 1

we need to find

Δf(x) = ?

we already know that

Δx = 0.1 , because Δx = x2 - x1 = 1.6 - 1.5 = 0.1

we also know how f(x) varies,

Δf(x) = 3.5 * Δx

so let's replace Δx = 0.1 to find Δf(x)

`\begin{gathered} \Delta f\mleft(x\mright)=3.5\cdot\Delta x \\ \Delta f\mleft(x\mright)=3.5\cdot0.1 \\ \Delta f\mleft(x\mright)=0.35 \end{gathered}`

Now, let's find f(1.6)

- Since this is a linear function, it is given by the following general equation

f(x) = m*x + b , we already know m = 3.5, but we don't know the value of b. We can find b by replacing:

f(1.5) = 2.8

`\begin{gathered} f(1.5)=3.5\cdot1.5+b=2.8 \\ 5.25+b=2.8 \\ b=2.8-5.25 \\ b=-2.45 \end{gathered}`

- now we have b = -2.45, and m = 3.5, we can find the value for any x,

let's find f(1.6) =

`\begin{gathered} f(1.6)=(3.5\cdot1.6)-2.45 \\ f(1.6)=3.15 \end{gathered}`

therefore, f(1.6) = 3.15

- As indicated above, the function formula for f(x) is:

`f(x)=3.5x-2.45`