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

Question

asked Oct 12, 2023 56.1k views

1 Answer

Autocrab · Answer 1 · 2023-10-17T05:59:56+0000

The given function is

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