calculus for another week yeerddd me.
Disks
Formula: piS(equation)^2dx
Find Bounds (How?)
Integrate using Definite Integration
Washers
Formula: piS[(top equation)^2-(bottom equation)^2]dx
Find Bounds
Integrate using Definite Integration
First derivative test:
The problem will give u a function and you have to take the derivative of that function and solve for the x values. Then you plug those x values into intervals between negative infinity and infinity. Then plug in numbers between those intervals into the derivative to find if the function is a max, min, increasing or decreasing.
Second derivative test:
You take the derivative of the function twice and solve for the x values once more. Set those values up into intervals between negative infinity and infinity. Plug in a number between these intervals into the second derivative to see if it is concave up, concave down, or a point of inflection.
Product Rule:
You take the derivative of the first and then leave the second as is, then added to the original first and take the derivative of the second.
Related rates-
1.Identify all variables
2. Identify what you are looking for
3. Sketch & label that graph
4. write an equation using all of the variables
5. Take the derivative of this equation
6. Substitute everything back in
7. Solve
i suck at tangent lines
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To find the equation of a tangent line, you need a point and a slope.
ReplyDeleteYou can be given a x-value only and have to find y, which you do by plugging x into the original.
To find the slope, take the derivative of the equation and plug in the x value given.
Once you have your slope and point, plug into point slope form, which is y-y1 = m (x-x1)
Example: 4x^3 - 7x^2 at x=3
plug in x to find y: 4(3)^3 - 7(3)^2 = 45
slope: 12x^2 - 14x
12(3)^2 - 14(3) = 66
Point slope: y-45 = 66 (x-3)