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[DOC File]Calculus 1 Lecture Notes, Section 2.9
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First derivative of the graph produced by parametric equations: If , then . Note: If , then the graph has a horizontal tangent line. ... t x y Comment 0 2 1 “starting point” (/6 3/2 Cusp point (/2 0 1 Midpoint of curved leg 5(/6 3/2 Cusp point 7(/6 -1/2 Midpoint of curved leg 3(/2 0 -3 Cusp point 11(/6 -1/2 Midpoint of curved leg 2( 2 …
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[DOCX File]November 12, 1997
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2. A projectile is fired directly upward from the ground with an initial velocity of 112ft/sec. Its distance above the ground after t seconds is 112t-16t2 feet. Find the velocity of the projectile at t = 2, t=3, and t=4. When does the projectile hit the ground? Find the velocity at the instant it hits the ground. 3.
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[DOCX File]MA-C2 Differential calculus Y12
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Definition of Derivative Worksheet. Use the definition of a derivative to find the derivative of each function at the point indicated. 1. y = 2x2 – 5x – 4 at x = 5 2. y = at x = 3. Find the generalized derivative for the function. Remember that means your answer will be in terms of ‘t’. 3. h(t) = -16t² + 60t + 80. 4.
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[DOCX File]Louisiana State University
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Definition of Derivative Worksheet. Use the definition of a derivative to find the derivative of each function at the point indicated. 1. y = 2x2 – 5x – 4 at x = 5 2. y = at x = 3. Use our same limit of slopes definition to find the generalized derivative for the function. Remember that means your answer will …
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The Derivative of sec2x – DerivativeIt
Lesson 13: The Second Derivative. For a function f, the derivative of f is called and itself is a function. The derivative of a function tells you whether a function is increasing or decreasing over an interval. The second derivative of f is written (read as “f double-prime”) or which means , the derivative with respect to x …
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[DOC File]Chapter 3 – Part 1: THE DERIVATIVE
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Topic 2: The Derivative Function The slope of the lines tangent to the graph of a function (or the instantaneous rate of change of the function) is called the derivative of the function. For convenience, we will let h represent ∆x when defining the derivative.
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[DOC File]Definition of Derivative Worksheet
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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]Definition of Derivative Worksheet
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Theorem 9.6 (Corollary #2 to the Mean Value Theorem): If f ( (x) = g ( (x) for all x in some open interval I, then for some constant c, f (x) = g(x) + c for all x ( I. Picture: Practice: Find all functions that have a derivative equal to 3x2 + 1. Find all functions that have a derivative equal to x4 + 3x.
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[DOC File]Lesson 13: The Second Derivative
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Students need to run a similar investigation into d dx (cos f (x)) =- f '(x)sin⁡ f (x) Lead students to use the quotient rule to determine the derivative d dx (tan x)= sec 2 x by using the identity tan x = sin x cos x. Use this result to lead students to apply the chain rule to determine d dx (tan f x)= f ' x sec 2 f(x)
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Derivative of sec 2 x