Post Number Eighteen

For my first post of the holidays, I’m gonna talk about the early weeks of calculus. Hopefully these blogs keep my grade up. The first thing we learned when we first started calculus were derivatives. Although confusing at first, repetition made them sooo easy! We learned many different derivative formulas, some including product rule, quotient rule, chain rule, sum and difference rules, trig function rules, inverse rules, and also quadratics. An example of taking a derivative of a quadratic is 3x^4 + 5x^3 – 2x^2 + x + 1

Taking a derivative of quadratics is easy, simply multiply the exponent to the coefficient and the exponent becomes one less. Therefore, the derivative of the equation given earlier would be 12x^3 + 15x^2 – 4x + 1.

Steps for Product Rule: UV = u(v’) + v(u’)
Copy the first.
Times the derivative of the second
+
Copy the second
Times the derivative of the first

Steps for Quotient Rule: U/V = (v(u’) – u(v’))/ v^2
Copy the bottom
Times the derivative of the top
-
Copy the top
Times the derivative of the bottom
All over the bottom squared

First Derivative Test:

Take the derivative of the original problem
Set the first derivative equal to 0
Solve for x and create intervals for x
Pick a number in the intervals then plug that number in the first derivative for x
Solve the equation

I understand the steps for the first derivative test, but I have trouble applying it for some reason. It used to be so easy, but now I can’t seem to solve problems like these. I think I get lost at the interval part.
Other things I still don’t understand are optimization and angle of elevation.
Hope everyone has a great Christmas :)