- Find the first derivative of the equation
- Set the derivative equal to zero
- Solve for the variable
If there are two equations, you can use substitution to get it to one equation to find the derivative, then once you solve for the variable in that equation, you can plug it into the other equation to find the second variable.
If there are multiple solutions, you can determine which is the correct one for the problem based on which is possible in the situation or which is the max/min (a problem will ask for the smallest (min) or largest (max) possible answer).
This process will allow you to use the slope to determine the best answer for the problem, either the smallest or the largest possible.
2. Find the point on the line y=2x+3 that is closest to the origin.
This process involves plugging the equation for y into the distance formula (after already having plugged in the coordinates of the origin). Once the equation is simplified, the power rule can be used to find the derivative, in order to find the smallest distance (minimum) from the origin. Once the derivative is set equal to zero, the value for x can be found. The value for x can then be plugged into the equation of the line to find the value for y.
3. Based on this derivative:
Two examples of what the function could have been are:
I like how on number 1 you discussed situations in which you aren't just simply finding the derivative or solving for one answer.
ReplyDeleteIN the very last example on the blog it appears you have a typo, or else you need to explain how 2x^3 equals 5x^2-x+12. Otherwise good job
ReplyDeletethanks, Dane
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