Question

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

Answer 1

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

$g^{\operatorname{\prime}\operatorname{\prime}}(-5)=-162$