y6-5-4-3-2-1.12347Graph of gThe figure above shows the graph of the differentiablefunction g and the line tangent to the graph of g at the point(3, 4). Let f be the function given by f (x) = | g(t) dt.Let h be the function with first derivative given byh' (x) =graph of h at x = a is parallel to the line tangent to thegraph of f at x = 3, what is the value of a ?= xecos a for 0 < x < 7. If the line tangent to the0.1871.1154.3354.577LOlo

Graph of G is given.We need to find the value of a by using the given conditions.Below find the…

Answered: y 6- 5 4. 3+ 2 1 1 3 4 5 6. 7 Graph of…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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1. (#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…
find the derivative
4.1(1) Determines the derivative of each function.
A function f satisfies the following conditions. f(-3) = 2, f' (-3) = 0, f(-1) = 5, f' (-1) = 0, f (0) = 0, f' (0) = 0, f' (2) = -1 First sketch a possible graph of such a function and then sketch the graph of its derivative.
The graphs of f and g are shown. Let h(x) = f(g(x)) and s(x) = g(f(x)). y 15 10 5 -2 4 6. 10 (a) Write an equation for h'(x) in terms of f(x), g(x), f'(x), and g'(x). O h'(x) = g'(f'(x))f'(x) O h'(x) = g'(f(x))f'(x) h'(x) = f'(g'(x))g'(x) h'(x) = f'(g(x))gʻ(x) O h'(x) = f'(g'(x))g(x) O h'(x) = g'(f'(x))f(x) Find h'(3). (If an answer does not exist, enter DNE.) (b) Write an equation for s'(x) in terms of f(x), g(x), f'(x), and g'(x). O s'(x) = f'(g(x))g'(x) O s'(x) = g'(f'(x))F'(x) O s'(x) = f'(g'(x))g'(x) s'(x) = g'(f(x))f'(x) s'(x) = f'(g'(x))g(x) s'(x) = g'(f'(x)){x) Find s'(7). (If an answer does not exist, enter DNE.)
The graph of the derivative of a function f is shown to the right. The graph has horizontal tangent lines at x = -1, x= 1, and x = 3. At which of the following values of x does f have a relative maximum? (A) -2 only 3+ (В) -2, 1, and 4 2+ (C) 4 only (D) -1 and 3 only -1 Graph of f' Pictured to the right is the graph of h' (x) , the derivative of a function, h(x). Which of the following statements is/are true? Graph of h'(x) I. The graph of h(x) has a horizontal tangent when x = 3. II. The graph of h(x) is increasing on the interval (-∞, 2). - -2 1 1 2 4 III. The graph of h(x) is decreasing on the interval (-∞0, 3). (A) I only (В) П only (C) I and II only (D) I and III only The function f has the property that f(x),f'(x), and f"(x) are negative for all real values of x. Which of the following could be the graph of f? (A) (В) (C) (D) (E)
9. [Essay] Find the derivative of y * sign 3a* (x? – 3x + 1).
The function g(x) is obtained by shifting the graph of y=x2. (a) If g(3)=36, give a possible formula for g when g is the result of applying only a horizontal shift to y=x^2.
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