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6. Let f(x) = x³ + 3x +1. a. Find a simplified expression for f(x + h) and f(x + h) − ƒ(x). b. Find f'(x). c. Calculate f'(-1) and f(1). What do these values tell you about the tangent lines at the points with a values 1 and -1?

6. Let f(x) = x³ + 3x +1. a. Find a simplified expression for f(x + h) and f(x + h) − ƒ(x). b. Find f'(x). c. Calculate f'(-1) and f(1). What do these values tell you about the tangent lines at the points with a values 1 and -1?

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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6. Let f(x) = x³ + 3x + 1. a. Find a simplified expression for f(x + h) and f(x + h) – f(x). b. Find f'(x). c. Calculate f'(-1) and f(1). What do these values tell you about the tangent lines at the points with a values 1 and -1?
Transcribed Image Text:6. Let f(x) = x³ + 3x + 1. a. Find a simplified expression for f(x + h) and f(x + h) – f(x). b. Find f'(x). c. Calculate f'(-1) and f(1). What do these values tell you about the tangent lines at the points with a values 1 and -1?
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(6)  f(x)=x3+3x+1(a+b)3=a3+b3+3ab2+3a2b

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