Today in class we continued on the topic of related rate problems. We started out with a wire that we could cut and form a triangla and a square with the remaining peices. We wanted to maximize the volume that the wire enclosed. We made an equation for the area and solved for the first derivitive. we set that to 0 and solve. We ended up with a minimum on the interval from 0 to 10. This caused us to believe that the maximum in that domain would be at o or 10. we found that 0 maximized the volume so the wire should just make a square to get the most vollume. We also did a related rate problem about a person walking to a village through sand and on a sidewalk with different speeds on both. We used the same method of solving the prior equation.
Today, Dec. 4, we first received our quizzes. Then, we discussed the mean value theorum, which basically states that for any differentiable, continuous portion of a function, the slope of the secant line must match an instantaneous slope on the curve. The mean value theorum, which was proved in the early 1800s, helped end the discussion and prove that calculus isn't just lucky. We will use it next week to prove Lopitals Rule. We then applied the theorum to problems, finding at which x, between a and b, is the instintaneous velocity equal to the secant line. We tackled a few AP problems, including one that involved factoring with e^x in the equation.
Date Friday, Dec 5th We walked into class and received our quizzes on related rates. There was a brief discussion concerning the answers. After this we proceeded onto talking about the “power of using both the first and second derivative to find local maximums and minimums.” In other words, f’(x) = 0, means that there is some kind of max or min, and the sign of f’’(x) (+ or -) tells us about the graphs concavity at a particular point. After this we moved on to something new, parametric equations. These equations have to do with positions at different intervals of time. They separate motion into a two dimensional analysis, in which the horizontal and vertical are independent. We also discussed the meaning of dy/dx, naming it the slope of the tangent line. At the end we received a worksheet with a graphing investigation.
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Today in class we continued on the topic of related rate problems. We started out with a wire that we could cut and form a triangla and a square with the remaining peices. We wanted to maximize the volume that the wire enclosed. We made an equation for the area and solved for the first derivitive. we set that to 0 and solve. We ended up with a minimum on the interval from 0 to 10. This caused us to believe that the maximum in that domain would be at o or 10. we found that 0 maximized the volume so the wire should just make a square to get the most vollume. We also did a related rate problem about a person walking to a village through sand and on a sidewalk with different speeds on both. We used the same method of solving the prior equation.
Today, Dec. 4, we first received our quizzes. Then, we discussed the mean value theorum, which basically states that for any differentiable, continuous portion of a function, the slope of the secant line must match an instantaneous slope on the curve. The mean value theorum, which was proved in the early 1800s, helped end the discussion and prove that calculus isn't just lucky. We will use it next week to prove Lopitals Rule. We then applied the theorum to problems, finding at which x, between a and b, is the instintaneous velocity equal to the secant line. We tackled a few AP problems, including one that involved factoring with e^x in the equation.
Date
Friday, Dec 5th
We walked into class and received our quizzes on related rates. There was a brief discussion concerning the answers. After this we proceeded onto talking about the “power of using both the first and second derivative to find local maximums and minimums.” In other words, f’(x) = 0, means that there is some kind of max or min, and the sign of f’’(x) (+ or -) tells us about the graphs concavity at a particular point.
After this we moved on to something new, parametric equations. These equations have to do with positions at different intervals of time. They separate motion into a two dimensional analysis, in which the horizontal and vertical are independent. We also discussed the meaning of dy/dx, naming it the slope of the tangent line.
At the end we received a worksheet with a graphing investigation.
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