This week we took a test and studied alot.
One thing that i understand in calculus is related rates.
First you read your problem and dertimne what you are givin. Be sure to watch out if they give you something like ten miles/Hr, that you put that as a rate (dr/dt). Then you sketch and label your problem. Usually means you draw a traiangle. After that you set up your equation and take the derivative. when taking the derivative you have to be sure to take it with respect to time. When you do this you plug in your givins and solve for your unknown. Be sure when solving you only have one unknown. After you plug in your left with a simpel equation that can be easily solved.
One thing that i dont understand to much in calc is things such as tangent lines and limits when looking at the graph. I dont know but i guess i just didn't pick up these lessons. Tangent lines just mess with me. I know you take the derivative but once i do that i get lost and confused when plugging into slope or which ever formula it is.
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To find the equation of a tangent line, you are usually given an equation and a x value.
ReplyDeleteThe first step i do is to find my y value. You do this by plugging in your x value into the original equation.
Then take the derivative of your equation.
Once you have that, plug your x value in for x and solve.
Finally, plug your values into point slope form which is y-y1= m(x-x1)
Find the tangent line at y= 3x^3+ 4x^2 + 5 at x=1
Plug in x to find your y: 3(1)^3+ 4(1)^2 +5 = 12
Take derivative: 9x^2 + 8x
Plug in x: 9(1)^2+ 8(1)= 17
Plug into formula: y-12=17(x-1)
you may have to solve the equation for y, if it is a multiple choice question.
The first thing i do for tangent lines is find the slope.
ReplyDeleteEveryone should know by now that that means to take a derivative. So take the derivative of your equation, plug in your x value, and solve. That is your "m".
The next thing i do is finding my y value. To do this you simply plug in your x value into the original equation.
Now that you have all the needed values, plug them into the point slope formula:
y - y1 = m(x - x1).
hope i helped ryan :)