Question

4) Find the derivative of g(x) = 6x2-2x + 9 at x = -2

Answer 1

The given function is

`g(x)=6x^2-2x+9`

We need to find the derivative of g(x), then

`\begin{gathered} g^(\prime)(x)=6(2)x^(2-1)-2(1)x^(1-1)+0 \\ g^(\prime)(x)=12x^1-2x^0 \end{gathered}`

Remember any variable to the power of 0 = 1

`g^(\prime)(x)=12x-2`

We need to find the derivative at x = -2, then substitute x by -2 in g'(x)

`\begin{gathered} g^(\prime)(-2)=12(-2)-2 \\ g^(\prime)(-2)=-24-2 \\ g^(\prime)(2)=-26 \end{gathered}`

The derivative of g(x) at x = -2 is -26