Advanced Placement Calculus 2016 Graphical Numerical Algebraic Fifth Edition Student Edition + Mathxl 1-year License
5th Edition
ISBN: 9780133314533
Author: Prentice Hall
Publisher: Prentice Hall
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The curve of a function f (x) is given in the figure below and you are asked to draw on it
a) Draw a tangent to the figure for x = 9 and explain in a few words what this line tells us about the curve of the function f (x).
b) When interpreting f'(9), it is said that the result gives an approximate change of the function when x is increased by 1. Why is the relation approximately? Explain and draw on the picture to explain the deviation in question.
c) Draw two secant lines between x = 9 and x = 6.5 otherwise on the one hand and x = 9 and x = 7 on the other. What is the usefulness of these profiles when discussing the instantaneous rate of change (e. Instantaneous Rate of Change) of the function in x = 9?
remall. We couldn
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• Let g be a function such that g(1) = -2 and g'(1) = 7.
• Let h be the function h(x) = VT.
F(2) = g(x) - h(z).
Let F be a function defined as
F'(1) =
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- The definition of the error function also defines an "error term" E(x, y). Find E(x, y) for the function f(x, y) = 3x² + 5y at the point (7,-7). Hint: See the definition of Differentiation in the textbook (link to textbook) Submit Question Darrow_forward1. (#11 Exam 1 Review) Find the equation of the line tangent to the graph of the function: f (x) = x-2x² at x = 1. You must use the Definition of the Derivative to obtain the derivative. 2. (#9 Exam 1 Review) Sketch the graph of the function g for which: g(0) = g(2) = g(4) = 0, g' (1) = g(3) = 0,g' (2) = -1, lim g(x) = ∞, and lim g(x) = -∞ x 5 x-1+ 3. State the three-part Definition of Continuity. 4. (#13 Exam 1 Review) The graph of f is given. State, with mathematically correct reasons, the values for which f is not differentiable. -2 VA 0 2 4 X (Description: Graph with three components. First component is horizontal line in the 2nd quadrant to x = -2. Sharp turn upwards in downward arc into the 1st quadrant and ends with open dot where x = 1. Second component is solid dot at x = 1 vertically below the open dot. Third component begins with open dot at x = 1 below the solid dot. The graph falls in downward arc shape into the 4th quadrant, takes a sharp turn at x = 3 and continues as…arrow_forwardIdentify a function f that has the given characteristics. Then sketch the function. f(2)= 8 f'(x) = 3,− ∞ < x < 00 Step 1 We are given f '(x) = 3, −∞ < x < ∞. This means the derivative of our function f is constant for all real numbers. Another way to think of this is that the slope of the tangent line to f is the same regardless of where we are on f. What type of function has a constant slope? quadratic linear exponential cubic Step 2 We determined that f is a linear function, and we know f '(x) is the slope. Write the general form of a linear function replacing the slope with f '(x). f(x) = mx + b f'(x) x + b = Submit x + b Skin (you cannot come back)arrow_forward
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