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[DOCX File]Department of Mathematics
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11. y= 12 x 4 -8 x 2 +5 e x 3 12. y= 1+ cos x sin x -1 . 13. y= sec x tan 1 x 14. y=4 sin 1+ x . Find the derivative of y with respect to x. 15. y= ln x 1+ x 16. y= e sin x ln x 2 +1 . 17. y= 100 x 2 18. y= ln e x - ln x
derivative of e y

[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.
derivative of x

[DOCX File]November 12, 1997
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Sec 2.6 – General Differentiation . Differentiation of Other Trig FunctionsName: Let’s try to prove the derivative of the function f x =tan x using trigonometric identities: f x = tan x = sin x cos x . Using the quotient rule determine the derivative of . f x .Let’s try to prove the derivative of the function . g x = sec x
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[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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[DOC File]Derivatives Homework - UH
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Question 2 20 points. Given: Give the following facts about this function: Domain. Range. End behavior – show with arrows. The x intercepts in point coordinate form. The y intercept in point coordinate form. The derivative: Use the quadratic formula to find zeros of the derivative, list them, and discuss the implications for the graph.
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[DOC File]Derivatives - UH
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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.
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[DOC File]Assignments Differentiation
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a. Is the function continuous at x = 2? 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.
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[DOC File]Math 131 E Lab 4: DERIVATIVE - MEASUREMENT OF CHANGE
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Part 2: THE DERIVATIVE AS A FUNCTION. Purpose. The purpose of this lab is to recognize a derivative as a function and to explore the relationship between a function and its derivative. Consider the graph in #8 of page 83 of your text. Sketch tangent lines to approximate the following. Carefully sketch tangent lines on f when x = -2, -1, 0, 1, 2 ...
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[DOC File]The First and Second Derivative Tests
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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 test gives the correct result. Ex. Use the second derivative test to find the local extreme points of . h(x) = 2x3 − 18x.
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E x 2 derivative