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QUESTIONS: 1. Given the graph of g(x), estimate g'(-4) b. a. 4 2 0 -2 + N 0 g'(-1.5) Graph of g 2 C. g'(o) d. g'(2.5)

QUESTIONS: 1. Given the graph of g(x), estimate g'(-4) b. a. 4 2 0 -2 + N 0 g'(-1.5) Graph of g 2 C. g'(o) d. g'(2.5)

Calculus: Early Transcendentals
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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please help me solve the problem #1 to 6 and I have also attached the answers she

ANSWERS: 1. a. 2 b. 0 2. a. Approximates the slope of the tangent line at x = a, using the slope of the secant line at x = a and x = a + h. C. -2 b. Approximates the slope of the tangent line at x = a, using the slope of the secant line at x = a + hand x = ah. This is how Nderiv works. c. Slope of the tangent line at x = a. 3. a. Sometimes 4. Corner Points, Vertical Tangent Lines, and Discontinuities 5. f'(x) = 4x-8 You should have used the definition. 7. a. f'(x) = 10x4 + 7 sin(x) C. 6. a. f'(x) = 3x²–5x+1, f"(x) = 6x-5 g(x) = b. Must be true d. 0 (x³ - 7) sec(x) tan(x) - 3x² sec(x) (x³ - 7)² e. f'(x) = 6(3x5 +8)515xª g. h'(x) = 4 sin³(2x5) cos(2x5)10x¹ b. x = 0.2324, 1.434 b. dy dx h. - d. h'(x)=-4csc²(4x) ds dt C. X = 6x tan(x) + 3x² sec²(x) f. g(x) = 6x cos(6x³) – 3x²[18x² sin(6x³)] = et³ (3t³ + 1) t3 56
Transcribed Image Text:ANSWERS: 1. a. 2 b. 0 2. a. Approximates the slope of the tangent line at x = a, using the slope of the secant line at x = a and x = a + h. C. -2 b. Approximates the slope of the tangent line at x = a, using the slope of the secant line at x = a + hand x = ah. This is how Nderiv works. c. Slope of the tangent line at x = a. 3. a. Sometimes 4. Corner Points, Vertical Tangent Lines, and Discontinuities 5. f'(x) = 4x-8 You should have used the definition. 7. a. f'(x) = 10x4 + 7 sin(x) C. 6. a. f'(x) = 3x²–5x+1, f"(x) = 6x-5 g(x) = b. Must be true d. 0 (x³ - 7) sec(x) tan(x) - 3x² sec(x) (x³ - 7)² e. f'(x) = 6(3x5 +8)515xª g. h'(x) = 4 sin³(2x5) cos(2x5)10x¹ b. x = 0.2324, 1.434 b. dy dx h. - d. h'(x)=-4csc²(4x) ds dt C. X = 6x tan(x) + 3x² sec²(x) f. g(x) = 6x cos(6x³) – 3x²[18x² sin(6x³)] = et³ (3t³ + 1) t3 56
QUESTIONS: 1. Given the graph of g(x), estimate g'(-4) a. a. a. b. 4 2 a. b. 0 C. d. -2 -4 b. g'(-1.5) 0 2. Explain what each of the formulas mean f(a+h)-f(a) h Graph of 2 4 b. C. g'(o) f(a+h)-f(a-h) 2h C. 3. Determine whether the following statements MUST be true or are at least SOMETIMES false. Justify your answers. Find f'(x), and f''(x). Find the relative extremes of f(x). Find the inflection points of f(x). Make an accurate graph of f(x). d. g'(2.5) lim_f(a+h)-f(a) h h→0 If f is continuous at a point x, then it is differentiable at x. If f is differentiable at a point x, then it is continuous at x. 4. List the ways a function is not differentiable. 5. Let f(x) = 2x² – 8x + 1, compute f'(x) by using the definition. Show your work. 6. Let f(x) = x³ -2.5x² + x + 8
Transcribed Image Text:QUESTIONS: 1. Given the graph of g(x), estimate g'(-4) a. a. a. b. 4 2 a. b. 0 C. d. -2 -4 b. g'(-1.5) 0 2. Explain what each of the formulas mean f(a+h)-f(a) h Graph of 2 4 b. C. g'(o) f(a+h)-f(a-h) 2h C. 3. Determine whether the following statements MUST be true or are at least SOMETIMES false. Justify your answers. Find f'(x), and f''(x). Find the relative extremes of f(x). Find the inflection points of f(x). Make an accurate graph of f(x). d. g'(2.5) lim_f(a+h)-f(a) h h→0 If f is continuous at a point x, then it is differentiable at x. If f is differentiable at a point x, then it is continuous at x. 4. List the ways a function is not differentiable. 5. Let f(x) = 2x² – 8x + 1, compute f'(x) by using the definition. Show your work. 6. Let f(x) = x³ -2.5x² + x + 8
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