Question

Given the function g(x) = 6x ^ 3 + 9x ^ 2 - 360x , find the first derivative, g^ prime (x)

Answer 1

Step-by-step explanation:

The function is given below as

`g(x)=6x^3+9x^2-360x`

To find g'(x) , we will have

`\begin{gathered} g(x)=6x^(3)+9x^(2)-360x \\ g^(\prime)(x)=18x^2+18x-360 \end{gathered}`

Hence,

The final answer is

`g^(\prime)(x)=18x^(2)+18x-360`

Part 2:

Find g''(x)

To find g''(x) we will so the calculation below

`\begin{gathered} g^(\prime)(x)=18x^(2)+18x-360 \\ g^(\prime)^(\prime)(x)=36x+18 \end{gathered}`

Hence,

The final answer is

`g^(\prime)^(\prime)(x)=36x+18`

Part 3:

Evaluate g''(-5)

To do this, we will put x= -5 in g''(x)

`\begin{gathered} g^(\prime)^(\prime)(x)=36x+18 \\ g^(\prime\prime)(-5)=36(-5)+18 \\ g^(\prime\prime)(-5)=-180+18 \\ g^(\prime\prime)(-5)=-162 \end{gathered}`

Hence,

The final answer is