Derivative of e to the negative x
[DOC File]AP Calculus Assignments: Derivative Techniques
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nDeriv(e^(X),X,X)) What is the derivative of ? If the graph doesn’t do it for you, check the tables. ... Why is it negative? 8. Review the two limit definitions of the derivative f '(a). 9. Kenny was given the function y = xlnx for x ( [1, e] and asked to find the rate of change of y with respect to x. He did .
[DOC File]AP Calculus Free-Response Questions
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1 < x < 3 negative negative. a. What are the x-coordinates of all absolute maximum and minimum points of f on the interval ... f ’’(0) = 0. Let g be a function whose derivative is given by g ’(x) = e-2x(3f(x) + 2f ’(x)) for all x. a. Write an equation of the line tangent to the graph of f at the point where x = 0. b.
[DOC File]2003 AP Calculus AB Exam Section 2
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If the second derivative is negative, the first derivative is decreasing, meaning that the distance between the y values is decreasing. The answer is (B). A particle moves along the x-axis so that at any time t > 0, its acceleration is given by . If the velocity of the particle is 2 at time t = 1, then the velocity of the particle at time t = 2 is
[DOC File]DERIVATIVES
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If we denote y = f (x), then f ′(a) is called the derivative of f, with respect to (the independent variable) x, at the point x = a. Recall that the value of this limit is, if it exists, is the slope of the line tangent to the curve y = f (x) at the point x = a.
[DOC File]Assignments Differentiation
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b. Does the function have a derivative at x = 2? Explain. 6. Graph the function ƒ(x) = . Does it have a derivative at x = 2? Explain. Hint: it may help to zoom in several times on the point (2, 0). 7. Kenny was asked about the derivative of the function shown at right. Kenny said the derivative was negative and increasing. What happened?
[DOC File]Derivatives
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You bet and, more, each tangent line has a slope…the derivative at that number for x. So, using the quotient rule, we can calculate the derivative: The top polynomial is (x + 6) and it’s derivative is 1. The bottom polynomial is (x ( 2) and it’s derivative is 1. Now, at x = 5, the graph point is ( 5, 11/3) and the slope of the tangent line is
[DOC File]Average Rate of Change vs
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2 Sketch the graph of a function with a constant negative derivative when x0, a root at -1 and not differentiable at 0. LESSON #4. Cw. Draw the derivative worksheet- talk about increasing and decreasing. HW. Page 3 of packet- both sides. 1. 2. Find the derivative using the limit process f(x)=5-x2 ...
[DOC File]COSTS OF PRODUCTION
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The Second order condition (SOC): Each second order derivative must be negative (), but also For a minimum, each second order derivative must be positive (), and If the latter condition is not satisfied, i.e., if then it is a saddle point. That is, the point that meets the first order conditions is neither a minimum nor a maximum. Example
[DOC File]Calculus 1401: Exam 2
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a) f is not continuous at x= a. b) f is continuous but not differentiable at x= b. c) f’ is positive at x= c. d) f’ is negative at x= d. e) f’ is zero at x= e. f) f’ does not exist at x= f. 10. Please find the derivative for each of the following functions (do not simplify unless you think it is helpful). 11. Find the equation of the ...
[DOC File]The First and Second Derivative Tests
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If the second derivative test fails, then the first derivative test must be used to classify the point in question. Ex. f (x) = x2 has a local minimum at x = 0. Ex. f (x) = x4 has a local minimum at x = 0. But the second derivative test would fail for this function, because f ″(0) = 0. The first derivative …
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