Question

For each function, calculate the derivative at a point using the limit definition

Answer 1

Each function is Gary okay

Answer 2

Given:

`f(x)=2x^2-3x`

To determine the derivative using the limit definition, we follow the process shown below:

`\begin{gathered} f(x)=2x^2-3x \\ f^(\prime)(x)=(2x^2)^(\prime)-(3x)^(\prime) \\ \text{Simplify} \\ =2(x^2)^(\prime)-(3x)^(\prime) \\ =2(2)x^(2-1)-3 \\ f^(\prime)(x)=4x-3 \end{gathered}`

Next, we plug in x=0 into f'(x)=4x-3:

`\begin{gathered} f^(\prime)(0)=4(0)-3 \\ \text{Simplify} \\ f^(\prime)(0)=-3 \end{gathered}`

Therefore,

`f^(\prime)(0)=-3`