Identify a function f that has the given characteristics. Then sketch the function. f(2)= 8 f'(x) = 3,00 < x < 0⁰ Step 1 We are given f '(x) = 3, -∞0 < x < ∞. This means the derivative of our function f is constant for all real numbers. Another way to think of this is that the slope of the tangent line to f is the same regardless of where we are on f. What type of function has a constant slope? O quadratic O linear exponential O O cubic Step 2 We determined that f is a linear function, and we know f '(x) is the slope. Write the general form of a linear function replacing the slope with f '(x). f(x) = mx + b = f'(x)x + b x + b Submit Skin (you cannot come back!
Identify a function f that has the given characteristics. Then sketch the function. f(2)= 8 f'(x) = 3,00 < x < 0⁰ Step 1 We are given f '(x) = 3, -∞0 < x < ∞. This means the derivative of our function f is constant for all real numbers. Another way to think of this is that the slope of the tangent line to f is the same regardless of where we are on f. What type of function has a constant slope? O quadratic O linear exponential O O cubic Step 2 We determined that f is a linear function, and we know f '(x) is the slope. Write the general form of a linear function replacing the slope with f '(x). f(x) = mx + b = f'(x)x + b x + b Submit Skin (you cannot come back!
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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Transcribed Image Text:Identify a function f that has the given characteristics. Then sketch the function.
f(2)= 8
f'(x) = 3,− ∞ < x < 00
Step 1
We are given f '(x) = 3, −∞ < x < ∞. This means the derivative of our function f is constant for all real numbers. Another way to think of this is that the slope of the
tangent line to f is the same regardless of where we are on f. What type of function has a constant slope?
quadratic
linear
exponential
cubic
Step 2
We determined that f is a linear function, and we know f '(x) is the slope. Write the general form of a linear function replacing the slope with f '(x).
f(x) = mx + b
f'(x) x + b
=
Submit
x + b
Skin (you cannot come back)
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