spring break was fun. now back to school.
Steps in order to optimize anything:
1. Identify primary and secondary equations. Primary deals with the variable that is being maximized or minimized. The secondary equation is usually the other equation that ties in all the information given in the problem.
2. Solve the secondary equation for one variable and then plug that variable back into the primary. If the primary equation only have one variable you can skip this step.
3. Take the derivative of the primary equation after plugging in the variable, set it equal to zero, and then solve for the variable.
4. Plug that variable back into the secondary equation in order to solve for the last missing variable. Check endpoint if necessary to find the maximum or minimum answers.
Finding absolute max/min
1. First derivative test
2. Plug critical values into the origonal function to get y-values
3. Plug endpoints into the origional function to get y-values
4. The highest y-value is the absolute maximum
5. The lowest y-value is the absolute minimum
*Remember that absolute maximums or minimums are written as a point, or simply as the y-value
First/second derivative tests.
1. Take a derivative
2. Set it equal to 0
3. Solve for x to find max, min, horizontal tangents, extrema (critical points)
4. Set up intervals using step 3.
5. Plug in first derivate
6. To find an absolute max/min plug values from #5 into original function
7. Check endpoints
Substitution takes the place of the derivative rules for problems such as product rule and quotient rule. The steps to substitution are:
1. Find a derivative inside the interval
2. set u = the non-derivative
3. take the derivative of u
4. substitute back in
tangent lines and me dont mix for some reason
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okay, i think i finally remember how to do them.
ReplyDelete1. plug in the x value to the original to get the y-value.
2. plug in the x value to the derivative to get the slope
3. put them all together in this form:
y-y = slope(x-x)
then simplify to how the problem wants it!
For tangent lines you will be given an x value and a function. To get the y value, plug in the x value into the original function to get it. The take the derivative of the function and plug in the x value to find the slope. Then plug everything into point-slope form y-y1=slope(x-x1). Hope this helps ya!
ReplyDeleteTANGENT LINES:
ReplyDelete1. plug in x-value to get your y-value
2. take the derivative of the function
3. plug in the x-value to find te slope
4. now plug into the formula y-y=slope(x-x)
simple..
ReplyDeleteget yvalue by plugging in xvalue, take derivative, plug in the xvalue to get the slope this time, now use pointslope formula
For a tangent line, you need to have a point and a slope.
ReplyDeleteSince you are usually given an x-value, plug the x-value into the original equation to find y.
Next, take the derivative of the equation and plug in the x-value to find the slope.
Once you have the slope and point, plug into the point slope formula which is y-y1= m (x-x1)
You may have to solve for y or put the equation in another form for it to match an answer choice.
Example: Write the equation to the line tangent to y = e^x+1 at x=0.
Plug in x: e^0+1 = e^1 = e
Your point is (0,e)
Take derivative: e^x+1
f' = e^x+1 (1)
plug in x: e^0+1 = e^1 = e
Point slope: y-e = e(x-0)
OR y = ex + e
Help with tangent lines!
ReplyDeleteFirst plug in your x value to get the y value if not given one, then take the derivative of the function. After taking the derivative, plug in the x value to get the slope. To finish, plug in to point slope form.
y - y1= m(x - x1)
For tangent lines you are usually given a function and a point, or both points. If you only have on poing, lets say x, you plug that into the origional function to find y. Whenever you have y, take the derivative of the function and plug x in to get your slope. Once you have your slope you have everything you need for your tangent line formula. You then plug you x, your y, and your slope into point slope form and you're done.
ReplyDelete