Derivative of x 2 x
[DOC File]AP Calculus Assignments: Derivative Techniques
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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. ... The evaluation must be done after the derivative …
[DOC File]Derivatives
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Take the derivative of f(x) and set it equal to zero: Note that there’s a common factor of twelve, divide it out: Use the Rational Root theorem and synthetic division to find that the factors of the derivative are. 12(x + 3)(x ( 2)(x + 1) So the turn around points are at x = (3, x = 2, and x = (1.
[DOC File]Assignments Differentiation
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AP Calculus HW: Derivative Concepts - 2. 1. Use your calculator to approximate the slope of at the point x = 2 and write an equation of the tangent line to the graph of f at that point. 2. A certain function f has f(4) = 3 and the slope of the tangent line to f at x = 4 is –1.25. a. Write the equation of …
[DOC File]DIFFERENTIAL CALCULUS
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a)(1/2, 1/2) b) (2,2) c) (-1/2, -1/2) d) none of these. 55. The slope of the tangent to the curve y = x2 – x at the point where the line y = 2 cuts the curve in the 1st quadrant is:
[DOC File]AP Calculus Free-Response Questions
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2x + 1, for x < 2, f(x) = x2 + k, for x > 2. a. For what values of k will f be continuous at x = 2? Justify your answer. b. Using the value of k found in part a, determine whether f is differentiable at x = 2. Use the. definition of the derivative to justify your answer. c. Let k = 4. Determine whether f is differentiable at x …
[DOC File]The Definition of the Derivative
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(2, 4) and (2 + (x, (2 + (x)2) ((x represents a small change in x) Find the slope of the tangent line by taking the limit of the last slope in (c) as (x ( 0; recall the slope of the tangent line is the derivative of the function at that point, so you have now found the derivative f ' (2).
[DOCX File]§2.1 Derivatives and Rates of Change
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§2.1 Derivatives and Rates of Change. Tangent Lines. axes, curve C. Consider a smooth curve C. A line tangent to C at a point P both intersects C at P and has the same slope as C at P. add line . t . The Tangent Line Problem
[DOC File]MTH101 2nd Quiz - NING
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Its anti – derivative is Sin(x) + x^2/2 + 10. Its anti – derivative is -Sin(x) + x^2/2 + 4. Question # 7 of 10 ( Start time: 09:06:54 PM ) Total Marks: 1. Integral of 5^2 is NOTE: x^n means ‘x’ to the power ‘n’ Select correct option: (1/3)5^3 10 25x. None of these. Question # 8 of 10 ( …
[DOC File]DERIVATIVES
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The derivative of a function of x is another function of x. Up until this point, derivatives of functions were calculated at some arbitrary, but fixed, point a. Notice from the previous examples that the expressions obtained can be evaluated at different values of a.
[DOC File]CALCULUS
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Suppose that the function f has a continuous second derivative for all x and that. Let g be a function whose derivative is given. by for all x. (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.
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