Equation of tangent line at point calculator
[DOC File]AP Calculus Assignments: Derivative Techniques
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8. Find the equation of the line tangent to at the point where x = 2. 9. Find the equation of the line tangent to at the point where x = 1. 10. A bug travels along the x-axis. Its position as a function of time is given by (x in meters, t in seconds; it’s a very fast bug) for t ( 0. a. Find the bug’s velocity as a function of time. b.
[DOC File]2006 AP Calculus AB – Part A (with calculator) - Solutions
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Now what’s this about the tangent line equation? Point-slope form! (I can feel it coming!)… y – y0 = m(x – x0) where the point is at x = 4. Be careful! We’re talking about a tangent to the graph of g (which we can’t see!) , forget the graph of f above! The point on g is (108, g(108)) and the slope m = is given by … Confusing!
[DOC File]1
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1. Consider the function y(x) defined implicitly by . Find the equation of the line tangent to the graph at the point (4, 0). Use your equation to find an approximate value for y when x = 4.1. 2. The graphs of function f, its antiderivative, F, and its second derivative, are shown in this plot: Write labels here (f, F, or )
[DOC File]CALCULUS BC
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(c) Write an equation for the line tangent to the graph of g at x = 3. Graph of f (d) Find the x-coordinate of each point of inflection of the graph of g on . Justify your answer. _____ 47. Consider the differential equation given by (a) On the axes provided, sketch a slope field for the given . differential equation at the indicated points.
[DOC File]Introduction to Tangent Lines using TI-Nspire CAS
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Graph the equation y = x3 + 2x2 - 3x – 4 on the window [-10, 10] by [-10, -10]. Draw a point on the curve, draw a tangent line through that point, and find the equation of the tangent line, using the TI-Nspire. To draw a point on the curve and draw a tangent through that point, refer to Activity 1.
[DOC File]Equations and Graphs
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As we get closer to we get closer to the actual slope of the tangent line, the value We call the slope of the tangent line at the point the derivative of the function at the point . Let’s make a couple of observations about this process. First, we can interpret the process graphically as finding secant lines from to other points on the graph.
[DOCX File]MATH 201 – CALCULUS I
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Write the equation of the tangent line to a curve at a given point. State and be able to use Rolle's and the Mean Value Theorems. Differentiate any algebraic or trigonometric function using the rules of differentiation, including implicit differentiation, and write answers in simplified form.
[DOC File]2007 AB Calculus Exam – Solutions
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(a) Using the tangent line (since we really don’t have the equation!) approximation… Tangent line? Point-slope form (as usual!) y – y0 = m (x – x0) So… Since the curve (see sketch above) is concave down, this is an overestimate. The tangent line is above the curve. (b) Related Rates! An easy one!
[DOC File]Section 1
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(Euclid) Given a secant line of a curve, as Q → P , the secant line approaches the tangent line at P, i.e., the tangent line is the limiting position. If P has coordinates (a, f(a)) and Q has coordinates (a + h, f(a+h)), then. and Example 1: Find the slope of the tangent line to the curve f(x) = 3 - 2x – 2x2 where x = 1.
[DOC File]CALCULUS BC
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(b) Find an equation of the tangent line to C at the point where t = 2. 7. A curve C is defined by the parametric equations. (a) Find in terms of t. (b) Find an equation of the tangent line to C at the point where t =. _____ On problems 8 – 10, find: (a) in terms of t.
[DOCX File]Mayfield City Schools
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Draw a tangent line at the point (-7, 8). Have the calculator display the coordinates of the point of tangency. Then have the calculator display the equation of the tangent line. Move the point of tangency so that it is at the point (-7, 8). Record the slope (round to the nearest integer) of the tangent line in the table above.
[DOC File]LOCAL LINEARITY: SEEING MAY BE BELIEVING
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Let be the line tangent to the graph of at . Find an expression for . Write an equation for line . Give the coordinates of a point that is on the graph of but is not on line . Give the coordinates of a point that is on line but is not on the graph of . An icicle is in the shape of a right circular cone.
[DOC File]EXTRA CREDIT: +5 points
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More Derivative and Tangent Line Problems. NO CALCULATOR!!! 1. The graph of the equation has a slope equal to 5 at exactly two points. Find the coordinates of the points. 2. Find the value of c , where the line l tangent to the graph of at ( 0 , 1 ) intersects the x-axis. 3. Find the equations of all lines through the origin tangent to the ...
[DOC File]CALCULUS
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(a) Write an equation of the line tangent to the graph of f at the point where . (b) Does g have a local maximum or a local minimum at ? Justify your answer. _____ 6. Conside the curve given by (a) Show that (b) Show that there is a point P with x-coordinate 3 at which the line tangent to the curve at P. is horizontal. Find the y-coordinate of P.
[DOC File]TREASURE HUNTING
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tangent line to f at Find the equation of the tangent line to f using where and the point is . Then plug in 0.1 into this line being sure to use an approximate sign. 50. Given the value of and the fact that the anti-derivative of f is F, find 1 Usually, this problem contains an antiderivative you cannot take.
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