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48. f" (t) = t² + 1/t², t>0, f(2)=3, f' (1)=2

48. f" (t) = t² + 1/t², t>0, f(2)=3, f' (1)=2

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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4.9: #48, please. For #48, find f given the equation.
Here is the transcribed text from the image, formatted for an educational website: --- ### Calculus Problems: Derivatives #### Problem Set: 42. \( f'(x) = (x + 1)/\sqrt{x}, \quad f(1) = 5 \) 43. \( f'(t) = \sec t (\sec t + \tan t), \quad -\pi/2 < t < \pi/2, \quad f(\pi/4) = \) 44. \( f'(t) = 3^t - 3/t, \quad f(1) = 2, \quad f(-1) = 1 \) - **Answer** ▼ 45. \( f''(x) = -2 + 12x - 12x^2, \quad f(0) = 4, \quad f'(0) = 12 \) - **Answer** ▼ 46. \( f''(x) = 8x^3 + 5, \quad f(1) = 0, \quad f'(1) = 8 \) 47. \( f''(θ) = \sin θ + \cos θ, \quad f(0) = 3, \quad f'(0) = 4 \) - **Answer** ▼ 48. \( f''(t) = t^2 + 1/t^2, \quad t > 0, \quad f(2) = 3, \quad f'(1) = 2 \) 49. \( f''(x) = 4 + 6x + 24x^2, \quad f(0) = 3, \quad f(1) = 10 \) - **Answer** ▼ 50. \( f''(x) = x^3 + \sinh x, \quad f(0) = 1, \quad f(2) = 2.6 \) 51. \( f''(x) = e^x - 2 \sin x, \quad f(0) = 3, \quad f(\pi/2) = 0 \) - **Answer** ▼ 52. \( f''(t) = \sqrt[3]{t} - \cos t, \quad f(0) = 2,
Transcribed Image Text:Here is the transcribed text from the image, formatted for an educational website: --- ### Calculus Problems: Derivatives #### Problem Set: 42. \( f'(x) = (x + 1)/\sqrt{x}, \quad f(1) = 5 \) 43. \( f'(t) = \sec t (\sec t + \tan t), \quad -\pi/2 < t < \pi/2, \quad f(\pi/4) = \) 44. \( f'(t) = 3^t - 3/t, \quad f(1) = 2, \quad f(-1) = 1 \) - **Answer** ▼ 45. \( f''(x) = -2 + 12x - 12x^2, \quad f(0) = 4, \quad f'(0) = 12 \) - **Answer** ▼ 46. \( f''(x) = 8x^3 + 5, \quad f(1) = 0, \quad f'(1) = 8 \) 47. \( f''(θ) = \sin θ + \cos θ, \quad f(0) = 3, \quad f'(0) = 4 \) - **Answer** ▼ 48. \( f''(t) = t^2 + 1/t^2, \quad t > 0, \quad f(2) = 3, \quad f'(1) = 2 \) 49. \( f''(x) = 4 + 6x + 24x^2, \quad f(0) = 3, \quad f(1) = 10 \) - **Answer** ▼ 50. \( f''(x) = x^3 + \sinh x, \quad f(0) = 1, \quad f(2) = 2.6 \) 51. \( f''(x) = e^x - 2 \sin x, \quad f(0) = 3, \quad f(\pi/2) = 0 \) - **Answer** ▼ 52. \( f''(t) = \sqrt[3]{t} - \cos t, \quad f(0) = 2,
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