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AP Review Questions Chapters 1 – 4
Complete the analogy. Clark Kent : Superman :: Bruce Wayne : 10 1.Hulk 2.Batman 3.Spiderman 4.Wolverine 1234
A calculator may not be used on these questions. Unless otherwise stated, the domain of a function is assumed to be all real numbers x for which f(x) is a real number.
If x 2 + xy = 10, then when x = 2, / /7 4.3/2 5.7/2 1234
If 1.ln 2 2.ln 8 3.ln nonexistent
What is the instantaneous rate of change at x = 2 of the function f given by /6 3.½ Answer Now 1234
A particle moves along the x- axis so that its position at time t is given by x(t)=t 2 -6t+5. For what value of t is the velocity of the particle zero?
If f(x)=sin(e -x ), then f(x) = cos(e -x ) 2.cos(e -x ) + e -x 3.cos(e -x ) - e -x 4.e -x cos(e -x ) 5.-e -x cos(e -x ) 1234
An equation of the line tangent to the graph of y = x + cos x at the point (0,1) is 1.y = 2x y = x y = x 4.y = x – 1 5.y = 0 :
If f(x) = x(x+1)(x-2) 2, then the graph of f has inflection points when x = 1.-1 only 2.2 only 3.-1 and 0 only 4.-1 and 2 only 5.-1, 0 and 2 only 10 Seconds Remaining 1234
If = ky and k is a nonzero constant, y could be 1.2e kty 2.2e kt 3.e kt kty ky2 +.5 Answer Now 1234
The function f is given by f(x)=x 4 +x On which of the following intervals is f increasing? 1.(-.707, ) 2.(-.707,.707) 3.(0, ) 4.(-,0) 5.(-,-.707)
If f(x) = tan(2x), then
1. If f(x) =, then f (x) = 2. Advanced Placement Calculus Semester One ReviewName:___________________ Calculator Active Multiple Choice 3. If x 3 + 3xy.
Problems on tangents, velocity, derivatives, and differentiation.
Warm Up A particle moves vertically(in inches)along the x-axis according to the position equation x(t) = t 4 – 18t 2 + 7t – 4, where t represents seconds.
1) Find the equations of all lines tangent to y = 9 – x 2 that passes through the point (1, 12).
Section 2.6 Day 2 Inflection Points and the Second Derivative I can describe the graph of f (x) given f (x). I can analyze the graph of f (x) in order.
Warm Up Determine the anti-derivative. Then differentiate your answer to check your work Evaluate the definite integral: 3.
Warm Up No Calculator 2) A curve is described by the parametric equations x = t 2 + 2t, y = t 3 + t 2. An equation of the line tangent to the curve at.
INTRODUCTORY MATHEMATICAL ANALYSIS For Business, Economics, and the Life and Social Sciences 2007 Pearson Education Asia Chapter 11 Differentiation.
3.9 Derivatives of Exponential and Logarithmic Functions.
Copyright © Cengage Learning. All rights reserved. 9.4 Parametric Equations.
Section c Let h be a function defined for all such that h(4) = -3 and the derivative of h is given by for. Write an equation for the line tangent.
Secant line between (a, f(a)) and (c, f(c)) (c, f(c)) y = f(x) (a, f(a)) x y Tangent line at (c, f(c)) Definitions (informal): 1.A secant line is a line.
AP Calculus AB Midterm Review. If, thenis A. B. C. D.
Section 2.5 Day 2 Critical Numbers – Relative Maximum and Minimum Points I can determine the key components of a function given the its derivative both.
1 CONCAVE UPWARDS g"(x) > 0. 2 CONCAVE DOWNWARDS g"(x) < 0 negative slope y = g(x) positive slope zero slope.
Chapter 2 Describing Motion: Kinematics in One Dimension.
Aim: Functions & Derivative Graphs Course: AP Calculus Do Now: Aim: What is the relationship between the graph of a derivative function and the graph of.
Graph of a Curve Continuity This curve is _____________These curves are _____________ Smoothness This curve is _____________These curves are _____________.
Warm Up 1)Sketch the graph of y = ln x a)What is the domain and range? b)Determine the concavity of the graph. c)Determine the intervals where the graph.
Warm up 1.Graph the equation of the line using slope & y-intercept 4x – 2y = 10.
Section 2.3 – Product and Quotient Rules and Higher- Order Derivatives.
Implicit Differentiation Related Rates Optimization Extrema Concavity Curve sketching Mean Value & Rolle’s Theorem Intermediate Value Theorem Linearization.
Polynomial Factors Polynomial Factor Theorem. 7/23/2013 Polynomial Factors 2 The Remainder Theorem Polynomial f(x) divided by x – k yields a remainder.
Graphs & Functions Strategies Higher Maths Click to start.
Warm Up Page 92 Quick Review Exercises 9, Rates of Change & Tangent Lines What youll learn Average rate of change Tangent to a curve Slope of.
While sitting at the beach, you count the number of waves that hit the beach during a certain amount of time. This measurement is most closely associated.
Copyright © Cengage Learning. All rights reserved. 4.6 Graphs of Other Trigonometric Functions.
Copyright © Cengage Learning. All rights reserved. 1.3 Graphs of Functions.
Rate of Change And Limits What is Calculus? Click to see more.
2.6 The Derivative By Dr. Julia Arnold using Tan’s 5th edition Applied Calculus for the managerial, life, and social sciences text.
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