Find f if f"(x) = 4 – 6x, f(0) = 3, and f(2) = -2. %3D Answer: f(x) =|

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...
icon
Related questions
Question
Find f if f"(x) = 4 – 6x, f(0) = 3, and f(2) = -2.
%3D
Answer: f(x) =|
Transcribed Image Text:Find f if f"(x) = 4 – 6x, f(0) = 3, and f(2) = -2. %3D Answer: f(x) =|
Expert Solution
Step 1

f"(x) = 4 - 6x , integrating the equation 

Using the formula ∫ xndx = xn+1n+1

∫ f''(x) dx = ∫ 4 dx - 6 ∫ x dx

f'(x) = 4x - 6x22 + c where c is integral constant

f'(x) = 4x - 3x+ c   .....(1)

integrating the equation (1)

∫ f'(x) dx = 4 ∫ x dx - 3 ∫ x2 dx + c ∫ 1 dx

f(x) = 4x22- 3x33 + cx + d  , where d is integral constant

steps

Step by step

Solved in 3 steps

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning