Tis' The Season Blog Post

1. Derivatives do not exists in corners, cusps, jumps, and asymptotes.

2. Take the derivative of the equation, but for the derivative of each constant, write "d of the constant" (For example: dy) over dx. Then solve for that constant. When deriving x, dx/dx will be equal to one, thus you do not have to write it while solving.
3. Writing the "dy/dx" or other constants while taking the derivatives of those constants.
4. I shared it.

2 Chainz Rule #TRU

1. f'(0) represents the critical point where the slope of the point is 0
2. Make a number line with values greater than and less than the x value you found. Plug and chug and find whether it is positive or negative. If it goes negative to positive, it is increasing. Positive to negative is decreasing.
3. Take the derivative of the outside function multiplied by the inside function multiplied by the derivative of inside function.
f(x)=(4-2x)^3
f"=3(4-2x)^2*-2 = -6(4-2x)^2
Tangent line at x=3
m=-24 (Plug 3 into derivative)
y= -8 (Plug 3 into original equation)
y+8=-24(x-3)
4. h'(-4)=f'(g(-4))g'(-4)

h'(-4)=f'(-5)g'(-4)

h'(-4)=20*2=40

Blog Post 4

1. f(x) 3- {sqr(x) where x is greater than or equal to 4
               {x^2+3 where x is less than 4
Plug 4 into each equation, approaching the left and right
Equation #1 comes to 19
Equation #2 comes to 1
They are not equal, therefore f(x) is not continuous

2. f(x)=2x^2+5x-3 [0,4]
Plug 0 and 4 into the equation
f(0) comes out to equal -3
f(4) comes out to equal 49
Since one is negative and the other is positive, there is indeed a solution

f(x)= -3x^2+14x-8 [-3,0]
Plug -3 and 0 into the equation
f(-3) comes out to equal -77
f(0) comes out to equal -8
Since they are both negative, a solution cannot be proven.

3. Two types - Different quotient and slope of a tangent line
Linear derivative - f(x)=2x-3 as x approaches 1
2x-3- f(1) / x-1
2x-3 - 1 / x-1
2x-2 / x-1
(x-1)(x+1) / x-1
x+1 = 2
A derivative is the slope of a line at a certain point
The hardest part is the difference quotient and doing the algebraic part of distributing the xs and hs.

4. Instantaneous velocity is the slope of one certain point. Average velocity is the average slope of a point.

Revised Calc Post 3

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Blog Post 3