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We are given f(x) = 3x² and f'(x) бх. (a) Find the instantaneous rate of change of f(x) at x = 2. (b) Find the slope of the tangent to the graph of y = f(x) at x = 2. (c) Find the point on the graph of y = f(x) at x = 2.

We are given f(x) = 3x² and f'(x) бх. (a) Find the instantaneous rate of change of f(x) at x = 2. (b) Find the slope of the tangent to the graph of y = f(x) at x = 2. (c) Find the point on the graph of y = f(x) at x = 2.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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2. [-/1 Points] DETAILS HARMATHAP11 9.3.007.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER We are given f(x) = 3x2 and f'(x) = 6x. (a) Find the instantaneous rate of change of f(x) at x = 2. (b) Find the slope of the tangent to the graph of y = f(x) at x = 2. (c) Find the point on the graph of y = f(x) at x = 2. (x, y) = (| Need Help? Read It Master It
Transcribed Image Text:2. [-/1 Points] DETAILS HARMATHAP11 9.3.007.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER We are given f(x) = 3x2 and f'(x) = 6x. (a) Find the instantaneous rate of change of f(x) at x = 2. (b) Find the slope of the tangent to the graph of y = f(x) at x = 2. (c) Find the point on the graph of y = f(x) at x = 2. (x, y) = (| Need Help? Read It Master It
Expert Solution
Step 1

Given:

f(x)=3x2 and f'x=6x

Step 2

1.

we have to calculate the rate of change at x=2.

f(x)=3x2 and f'x=6x

since

        the derivative is the slope of the tangent the instantaneous rate of change at general value x is given by 

f'x=6×2=12

2.

we have to find the slope of the tangent to the graph at x=2

The derivative is the slope of the tangent line. 

 

 

 

 

 

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