this week has been crazy tiring w/ homecoming and such but i still ended up gettin alot accomplished. this week we learned linearization. linearization has to do w/ the word approximate. anytime you see the word "approximate" in a problem. it means to use linearization.
the formula for linearization: f(x) = f(c) + f(c)(x-c)
we went over related rates and had a quiz on it.
you're given a problem like, you have a spherical object moving , rate of change is ___ and dy/dx = ____ so find dx/dt. that type of problem requires you to draw out the picture yourself.
but you can also be given a picture with the problem, which can be very helpful.
steps, once again, are:
1. first identify all variables in equation
2. figure out what you want to find(what you are solving the equation for)
3. dont forget to sketch and label! *extra points
4. write an equation involving all your variables(plug in)
5. take derivative
6. solve
im much beetter at optimization after doing it over and over again. i also know horiztontal tangents
Determine all values of x, if any, at which the graph of the function has a horizontal tangent.
y = x^3 + 12x^2 + 5
All you have to do is take the derivative and set it equal to zero, then solve for x.
3x^2
3x^2 + 24x = 0
3x( x + 8) = 0
X = 0, x = -8
im not too good at angles of elevation really. anyonoe wanna explain a problem?
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You can use SOHCAHTOA to get the angle and take the derivative. A good one to use is tan(theta) = y/x
ReplyDeleteyeah, for angle of elevation you use SOHCAHTOA and then take the derivative.
ReplyDeleteYou either use tan(theta) = x/y or you can use cos=x/hyp or sin = y/hyp if needed.
Don't forget they can change You can use tan theta = x/y and you have one of those variables constant or you can use something like sin = y/hyp or cos = x/hyp
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