Warm-Up- AP free response (No Calculator )

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Presentation transcript:

Warm-Up- AP free response (No Calculator ) 1. Given the function defined by : a) Find the zeros of the function b) Write an equation of the line tangent to the graph of f at x = -1. c) The point (a,b) is on the graph of f and the line tangent to the graph at (a,b) passes through the point (0, -8) which is not on the graph of f. Find the values of a and b.

Warm-Up- AP free response (No Calculator ) 1. Given the function defined by : a) Find the zeros of the function.

Warm-Up- AP free response (No Calculator ) 1. Given the function defined by : b) Write an equation of the line tangent to the graph of f at x = -1.

Warm-Up- AP free response (No Calculator ) 1. Given the function defined by : c) The point (a,b) is on the graph of f and the line tangent to the graph at (a,b) passes through the point (0, -8) which is not on the graph of f. Find the values of a and b.

More Practice 2. Given the function defined by a) Find the zeros of the function b) Write an equation of the line normal to the graph of f at x = 0. (A normal line is a line that is perpendicular to a tangent line at the point of tangency). Find the x- and y-coordinates of all points on the graph where the line tangent to the graph is parallel to the x-axis.

More Practice 2. Given the function defined by a) Find the zeros of the function

More Practice 2. Given the function defined by b) Write an equation of the line normal to the graph of f at x = 0. (A normal line is a line that is perpendicular to a tangent line at the point of tangency).

More Practice 2. Given the function defined by c) Find the x- and y-coordinates of all points on the graph where the line tangent to the graph is parallel to the x-axis.

Do this…No calculator 3. Given the function defined by for a) State whether the function is even or odd. Justify. b) Find f’(x) c) Write an equation of the line tangent to the graph of f at the point where x = 0.

Warm-Up 3. Given the function defined by for a) State whether the function is even or odd. Justify.

Warm-Up 3. Given the function defined by for b) Find f’(x)

Warm-Up 3. Given the function defined by for c) Write an equation of the line tangent to the graph of f at the point where x = 0.

Warm-Up- Calculator needed. A Watermelon is thrown upwards from a height of 1000 feet with an initial velocity of 10 feet per second. The height, s (measured in feet), at time, t (measured in seconds), is given by Justify your work for all parts. a. Find the average velocity on the interval [0, 4]. Don’t forget to write your units of measure. b. Find the instantaneous velocity when t = 4. Write your units of measure. c. How long does it take for the watermelon to hit the ground? Round to the nearest thousandth. d. Find the velocity of the watermelon when it hits the ground. Round to the nearest thousandth.

Warm-Up- Calculator needed. A Watermelon is thrown upwards from a height of 1000 feet with an initial velocity of 10 feet per second. The height, s (measured in feet), at time, t (measured in seconds), is given by Justify your work for all parts. a. Find the average velocity on the interval [0, 4]. Don’t forget to write your units of measure.

Warm-Up- Calculator needed. A Watermelon is thrown upwards from a height of 1000 feet with an initial velocity of 10 feet per second. The height, s (measured in feet), at time, t (measured in seconds), is given by Justify your work for all parts. b. Find the instantaneous velocity when t = 4. Write your units of measure.

Warm-Up- Calculator needed. A Watermelon is thrown upwards from a height of 1000 feet with an initial velocity of 10 feet per second. The height, s (measured in feet), at time, t (measured in seconds), is given by Justify your work for all parts. c. How long does it take for the watermelon to hit the ground? Round to the nearest thousandth.

Warm-Up- Calculator needed. A Watermelon is thrown upwards from a height of 1000 feet with an initial velocity of 10 feet per second. The height, s (measured in feet), at time, t (measured in seconds), is given by Justify your work for all parts. d. Find the velocity of the watermelon when it hits the ground. Round to the nearest thousandth.

Describe the derivative at each integer x-value shown on the graph below. (Positive, Negative, zero, or DNE)

49) B