Compute the derivative:
![\dfrac{\mathrm d}{\mathrm dx}\bigg[8x^3+2x^2-8\bigg]=24x^2+4x](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B8x%5E3%2B2x%5E2-8%5Cbigg%5D%3D24x%5E2%2B4x)
Set equal to zero and find the critical points:

Compute the second derivative at the critical points to determine concavity. If the second derivative is positive, the function is concave upward at that point, so the function attains a minimum at the critical point. If negative, the critical point is the site of a maximum.
![\dfrac{\mathrm d^2}{\mathrm dx^2}\bigg[8x^3+2x^2-8\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[24x^2+4x\bigg]=48x+4](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%5E2%7D%7B%5Cmathrm%20dx%5E2%7D%5Cbigg%5B8x%5E3%2B2x%5E2-8%5Cbigg%5D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B24x%5E2%2B4x%5Cbigg%5D%3D48x%2B4)
At

, the second derivative takes on the value of

, so the function is concave upward, so the function has a minimum there of

.
At

, the second derivative is

, so the function is concave downward and has a maximum there of

.
Step-by-step explanation:
it's not specific enough kid
Answer:

General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Algebra I</u>
- Functions
- Function Notation
- Coordinates (x, y)
<u>Calculus</u>
Derivatives
Derivative Notation
Antiderivatives - Integrals
Integration Constant C
Integration Rule [Reverse Power Rule]: 
Integration Property [Multiplied Constant]: 
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
Point (0, 18)

<u>Step 2: Find General Solution</u>
<em>Use integration</em>
- [Derivative] Rewrite:

- [Equality Property] Integrate both sides:

- [Left Integral] Integrate [Integration Rule - Reverse Power Rule]:

- [Right Integral] Rewrite [Integration Property - Multiplied Constant]:

- [Right Integral] Integrate [Integration Rule - Reverse Power Rule]:

- Multiply:

<u>Step 3: Find Particular Solution</u>
- Substitute in point [Function]:

- Simplify:

- Add:

- Rewrite:

- Substitute in <em>C</em> [Function]:

Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration
Book: College Calculus 10e
Answer:
i dont even know what congruent means
Step-by-step explanation:
step 1 throw your hands up then point them to the floor!
step 2 here is what to do now get down on all fours!
step 3 now bounce around its easy follow me!
step 4 go crazy now and beep beep like a sheep