Chapter 1 1.1 Lines Increments Δx, Δy Slope m = (y2 - y1)/(x2 - x1) Point-slope Equation y = m(x – x1) + y1 Slope-intercept equation y = mx + b General Equation Ax + By = C

Chapter 1 1.2 Functions and Graphs Function Vertical Line Test Even Functions f(-x) = f(x) Odd Functions f(-x) = -f(x) Symmetry Composite Functions f(g(x)) Types of Functions Piece, Absolute Value Domain and Range

Chapter 1 1.3 Exponential Functions f(x) = ax Domain and Range Rules for exponents ax ay = ax+y ax/ay = ax-y (ax)y = axy a-x=1/ax a0=1 Exponential Growth/Decay y = yObt/h The number e

Chapter 1 1.4 Parametric Equations x = f(t), y = f(t) Parametric Curves Circles, Ellipses, Hyperbolas Eliminating the parameter Substitution Trigonometric Identity

Chapter 1 1.4 Functions and Logarithms Domain and Range One-to-one, Horizontal Line Test Finding Inverses Logarithms y = logax if x = ay logaa = 1 loga1 = 0 logars = logar + logas logar/s = logar - logas logarc = c logar logbx = logax/logab

Chapter 1 1.5 Trigonometric Functions Graphs of Trigonometric Functions Period Transformations y = a f(b(x + c)) + d Identities Graphs of Inverse Trigonometric Functions

Chapter 2 2.1 Rates of Change Average and Instantaneous Speed Definition of a Limit Limit Properties Sandwich/Pinching Theorem

Chapter 2 2.2 Limits at Infinity Horizontal Asymptotes Vertical Asymptotes End Behavior 3 Rules

Chapter 2 2.3 Continuity Removable, Jump, Infinite, Oscillating Intermediate Value Theorem Properties of Continuous Functions

Chapter 2 2.4 Rates of Change and Tangent Lines Average Rates of Change Slope of a Curve Properties of Continuous Functions Normal and Tangent Lines

Chapter 3 3.1 Derivatives Definition Notation Graphing Derivatives from data/lines One Sided Derivatives

Chapter 3 3.2 Differentiability Nondifferentiable Breaks Corners Cusps Vertical Tangents Intermediate Value Theorem for Derivatives

Chapter 3 3.3 Rules for Derivatives Constant Rule Power Rule Constant Multiple Rule Sum and Difference Rule Product Rule Quotient Rule

Chapter 3 3.4 Velocity and Other Rates of Change Instantaneous Velocity Speed Acceleration Marginal Cost/Marginal Revenue

Chapter 3 3.5 Derivatives of Trigonometric Functions d/dx sin x = cos x d/dx cos x = -sin x d/dx tan x = sec2x d/dx cot x = -csc2x d/dx sec x = sec x tan x d/dx csc x = -csc x cot x

Chapter 3 3.6 Chain Rule d/dx f(g(x)) = f’(g(x))•g’(x) 2. 3. Finding Slope of Parametric Curves

Chapter 3 3.7 Implicit Differentiation Used when y cannot be solved in terms of x. Used for fractional exponents.

Chapter 3 3.8 Derivatives of Inverse Trigonometric Functions

Chapter 3 3.9 Derivatives of Exponential and Logarithmic Functions d/dx ex = ex d/dx ax = ax ln a d/dx ln x = 1/x d/dx logax = 1/a (ln a) Logarithmic Differentiation

Chapter 4 4.1 Extreme Values Absolute Extrema Extreme Value Theorem Local Extrema Critical Points

Chapter 4 4.2 Mean Value Theorem Mean Value Theorem for Derivatives f’(c) = (f(b) – f(a)) /(b – a) Increasing/Decreasing Functions Antiderivatives

Chapter 4 4.3 Connecting f’(x) with f’’(x) First Derivative Test Second Derivative Test Concavity Inflection Points

Chapter 4 4.4 Optimization Max-Min Problems Box Can Inscribed Figures Distance Fence

Chapter 4 4.5 Linearization Linearization L(x) = f(a) + f’(a)(x - a) Newton’s Method xn = xn-1 – f(xn)/f’(xn) Differentials dy = f(x) dx Absolute, Relative, and Percentage Change.

Chapter 4 4.6 Related Rates Balloon Ladder Box Conical Tank Highway Chase Rope