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ResourceSpotlight
In this activity, students will use the Calculator application to explore the Power Rule. For each of the four examples, they will first examine "true" statements about various derivatives of xn where n is an integer. They will observe patterns and use these patterns to create a rule for finding the derivative of xn with respect to x. They will then use their rule to create examples of their own.
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Texas Instruments, Inc.
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ResourceSpotlight
In this activity, students will observe a simulation of a record breaking bungee jump, consider a mathematical model of the height as a function of time, and take the derivative to determine points of interest like the minimum height, maximum velocity, acceleration, and maximum jerk. Students will algebraically, numerically, graphically and verbally investigate higher order derivatives.
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Texas Instruments, Inc.
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ResourceSpotlight
In this activity, students will observe a simulation of a record breaking bungee jump, consider a mathematical model of the height as a function of time, and take the derivative to determine points of interest like the minimum height, maximum velocity, acceleration, and maximum jerk. Students will algebraically, numerically, graphically and verbally investigate higher order derivatives.
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Texas Instruments, Inc.
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ResourceSpotlight
In this activity, students will observe the slopes of the secant line and tangent line as point Q on the function approaches the other point P. They will also determine the average rate of change for an interval and approximate the instantaneous rate of change using the slope of the secant line.
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Texas Instruments, Inc.
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ResourceSpotlight
In this activity, students will use the Calculator application to explore the Power Rule. For each of the four examples, they will first examine "true" statements about various derivatives of xn where n is an integer. They will observe patterns and use these patterns to create a rule for finding the derivative of xn with respect to x. They will then use their rule to create examples of their own.
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Texas Instruments, Inc.
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ResourceSpotlight
In this activity, students will explore the Mean Value Theorem. Students will find out when the tangent line is parallel to the secant line passing through the endpoints of an interval to help them find the values of c guaranteed to exist by the MVT. Students will also test functions where the hypotheses of the MVT are not met.
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Texas Instruments, Inc.
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ResourceSpotlight
In this activity, students will observe the slopes of the secant line and tangent line as point Q on the function approaches the other point P. They will also determine the average rate of change for an interval and approximate the instantaneous rate of change using the slope of the secant line.
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Texas Instruments, Inc.
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ResourceSpotlight
In this activity, students will explore the Chain Rule. Students are asked to make a conjecture of the derivative of f(x) = (2x + 1)2 based on the Power Rule. They are then asked to graph their derivative function and compare it to the graph of f´(x). They will then examine “true” statements about various derivatives of composite functions. They will observe patterns create a rule for finding the derivative of other composite functions.
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Texas Instruments, Inc.
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ResourceSpotlight
In this activity, students will explore the Mean Value Theorem. Students will find out when the tangent line is parallel to the secant line passing through the endpoints of an interval to help them find the values of c guaranteed to exist by the MVT. Students will also test functions where the hypotheses of the MVT are not met.
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Texas Instruments, Inc.
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A water balloon launched at time t=0 has vertical velocity v(t) = -32t + 40 ft/sec at time t seconds, with v>0 corresponding to upward motion. a) if the roof of the building is 30 ft above the ground, find an expression for the height of the water balloon above the ground at time t. b) what is the average velocity of the balloon b/ween t+1.5 and 3 sec? c) a 6 ft person is standing on the ground. how fast is the water balloon falling when it strikes the person on the top o the head?
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Tutor.com
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