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1.) Use a quick approximation to estimate the derivative of the given function at the indicated point. (Round your answer to three decimal places.) f(x) =x/4 -6 ; x=-1 f'(-1)= ?

1.) Use a quick approximation to estimate the derivative of the given function at the indicated point. (Round your answer to three decimal places.) f(x) =x/4 -6 ; x=-1 f'(-1)= ?

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
ChapterP: Prerequisites
SectionP.6: Analyzing Graphs Of Functions
Problem 6ECP: Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
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1.) Use a quick approximation to estimate the derivative of the given function at the indicated point. (Round your answer to three decimal places.)

f(x) =x/4 -6 ; x=-1

f'(-1)= ?

 

 

2.Consider the following function.

f(x) = 3x3; x = −1
(a) Use any method to estimate the slope of the tangent to the graph of the given function at the point with the given x-coordinate. (Round your answer to three decimal places.)


(b) Find an equation of the tangent line in part (a). 
y =
 
 


Sketch the curve together with the appropriate tangent line.
Use a quick approximation to estimate the derivative of the given function at the indicated point. (Round your answer to three decimal places.) f(x) = - 6; x = -1 4 f'(-1) =
Transcribed Image Text:Use a quick approximation to estimate the derivative of the given function at the indicated point. (Round your answer to three decimal places.) f(x) = - 6; x = -1 4 f'(-1) =
Consider the following function. f(x) = 3x³; x = -1 (a) Use any method to estimate the slope of the tangent to the graph of the given function at the point with the given x-coordinate. (Round your answer to three decimal places.) (b) Find an equation of the tangent line in part (a). HINT [See Example 2(b).] y = Sketch the curve together with the appropriate tangent line. y y 8- 6 4 4 2 2 X -4 -3 -2 -1 -2 1 2 3 4 -4 -3 -2 1 2 4 -4 -6 -8| y y 8- 8 6. 6 4 2 4 -3 -2 1 2 3 4 -3 -2 1 3 4 -2 -2 -4 -4 -6 -6 -8F 3. 2. 2.
Transcribed Image Text:Consider the following function. f(x) = 3x³; x = -1 (a) Use any method to estimate the slope of the tangent to the graph of the given function at the point with the given x-coordinate. (Round your answer to three decimal places.) (b) Find an equation of the tangent line in part (a). HINT [See Example 2(b).] y = Sketch the curve together with the appropriate tangent line. y y 8- 6 4 4 2 2 X -4 -3 -2 -1 -2 1 2 3 4 -4 -3 -2 1 2 4 -4 -6 -8| y y 8- 8 6. 6 4 2 4 -3 -2 1 2 3 4 -3 -2 1 3 4 -2 -2 -4 -4 -6 -6 -8F 3. 2. 2.
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