Suppose that f is a function given as f(x) = 3x² - 7x.Simplify the expression f(x + h).f(x + h) =Simplify the difference quotient,f(x+h)-f(x)h=f'(x) =limh→0f(x+h)-f(x)hThe derivative of the function at x is the limit of the difference quotient as h approaches zero.f(x+h)-f(x)h

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Answered: Suppose that f is a function given as…

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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Let g(x) = I f(t) dt, where f is the function whose graph is shown. y 2 N X X X X f XX Maple Generated Plot (a) Evaluate g(x) for x = 0, 2, 4, 6, 8, 10, and 12. g(0) = 2 g(2) = 0 g(4) = -2 g(6) = 6 g(8) = 2 g(10) = 4 g(12) = 6 12 t
Suppose that f is a function given as f(x) = 2x² + 7x - 2. Simplify the expression f(x + h). f(x + h) = Simplify the difference quotient, f(x+h)-f(x) h f(x+h)-f(x) h The derivative of the function at a is the limit of the difference quotient as h approaches zero. f'(x) = lim f(x+h)-f(x) h→0 h
problem is attached! please show all work because i have a few more problems like these so i want to make sure i understand how to solve this problem. please and thank you so much!
Select the statement that is false about the difference quotient. The difference quotient can be represented by f(x+h)−f(x)(x+h)−x or f(x+h)−f(x)h The difference quotient is a more general form of the average rate of change of a function on an interval h units long. The difference quotient describes the general behavior of a function over some interval h units long when the rate of change is not constant. As the value of h gets smaller and smaller, the value of the difference quotient becomes a better and better approximation of the average rate of change of a function f near (x,f(x)). As the value of h gets larger and larger, the value of the difference quotient becomes a better and better approximation of the average rate of change of a function f near (x,f(x)).

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Suppose that f is a function given as f(x) = 3x² - 7x. Simplify the expression f(x + h). f(x + h) = Simplify the difference quotient, f(x+h)-f(x) h = f'(x) =lim h→0 f(x + h) − f(x) h The derivative of the function at x is the limit of the difference quotient as h approaches zero. f(x+h)-f(x) h