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The function f' defined by the formula f(x + h) − f (x) h f'(x) = lim h→0 s called the derivative of ƒ with respect to x. The domain of f' consists of all x in the domain of f for which the limit exists.

The function f' defined by the formula f(x + h) − f (x) h f'(x) = lim h→0 s called the derivative of ƒ with respect to x. The domain of f' consists of all x in the domain of f for which the limit exists.

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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The function f' defined by the formula f(x+h)-f(x) h f'(x) = lim h→0 is called the derivative of f with respect to x. The domain of f' consists of all x in the domain of f for which the limit exists. (a) Use the definition to find ƒ'(x) when ƒ(x) = 3x². f'(x) = (b) Find the tangent line to the graph of ƒ(x) = 3x² at x = 9. Equation:
Transcribed Image Text:The function f' defined by the formula f(x+h)-f(x) h f'(x) = lim h→0 is called the derivative of f with respect to x. The domain of f' consists of all x in the domain of f for which the limit exists. (a) Use the definition to find ƒ'(x) when ƒ(x) = 3x². f'(x) = (b) Find the tangent line to the graph of ƒ(x) = 3x² at x = 9. Equation:
The function f' defined by the formula f(x+h)-f(x) h f'(x) = lim h→0 is called the derivative of ƒ with respect to x. The domain of f' consists of all x in the domain of f for which the limit exists. (a) Use the definition to find f'(x) when f(x) ƒ'(x)= = 20 x3 Equation: y (b) Find the tangent line to the graph of f(x) = = = = -2 10 x² 10 x² X at x = -1. Edit
Transcribed Image Text:The function f' defined by the formula f(x+h)-f(x) h f'(x) = lim h→0 is called the derivative of ƒ with respect to x. The domain of f' consists of all x in the domain of f for which the limit exists. (a) Use the definition to find f'(x) when f(x) ƒ'(x)= = 20 x3 Equation: y (b) Find the tangent line to the graph of f(x) = = = = -2 10 x² 10 x² X at x = -1. Edit
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