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Find the function f given that the slope of the tangent line to the graph of f at any point (x, f(x)) is f '(x) and that the graph of f passes through the given point. f'(x) = ex + 9x; (0,5) f(x) = ex + (9/2)x² + 4 X

Find the function f given that the slope of the tangent line to the graph of f at any point (x, f(x)) is f '(x) and that the graph of f passes through the given point. f'(x) = ex + 9x; (0,5) f(x) = ex + (9/2)x² + 4 X

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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Question
Find the function f given that the slope of the tangent line to the graph of f at any point (x, f(x)) is f '(x) and that the graph of f passes through the given point. f'(x) = ex + 9x; (0,5) f(x) = ex + (9/2)x² +4 X
Transcribed Image Text:Find the function f given that the slope of the tangent line to the graph of f at any point (x, f(x)) is f '(x) and that the graph of f passes through the given point. f'(x) = ex + 9x; (0,5) f(x) = ex + (9/2)x² +4 X
The velocity of a car (in feet/second) t sec after starting from rest is given by the function f(t) = 10√t (0 ≤ t ≤ 30). Find the car's position, s(t), at any time t. Assume s(0) = 0. s(t) = 5t² X
Transcribed Image Text:The velocity of a car (in feet/second) t sec after starting from rest is given by the function f(t) = 10√t (0 ≤ t ≤ 30). Find the car's position, s(t), at any time t. Assume s(0) = 0. s(t) = 5t² X
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