Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. (Simplify your answers completely.) f(x) = -x² + 6x Step 1: f(x + h) = 2 -h² - 3hx + 3h - x²+6x 2 Step 2: f(x + h) f(x) - = - - -h² − 6hx + 6h f(x + h) − f(x) - Step 3: = -h-6x+6 h Step 4: f'(x): = lim h→0 f(x + h) − f(x) h - = 6-6x Need Help? Read It Watch It SUBMIT ANSWER Viewing Saved Work Revert to Last Response

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter1: Functions
Section1.FR3: A Further Look: Definition Of A Function
Problem 8E
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Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. (Simplify your answers completely.)
f(x) = -x² + 6x
Step 1:
f(x + h)
=
2
-h² - 3hx + 3h - x²+6x
2
Step 2:
f(x + h) f(x)
-
=
- -
-h² − 6hx + 6h
f(x + h) − f(x)
-
Step 3:
=
-h-6x+6
h
Step 4:
f'(x):
= lim
h→0
f(x + h) − f(x)
h
-
=
6-6x
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Transcribed Image Text:Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. (Simplify your answers completely.) f(x) = -x² + 6x Step 1: f(x + h) = 2 -h² - 3hx + 3h - x²+6x 2 Step 2: f(x + h) f(x) - = - - -h² − 6hx + 6h f(x + h) − f(x) - Step 3: = -h-6x+6 h Step 4: f'(x): = lim h→0 f(x + h) − f(x) h - = 6-6x Need Help? Read It Watch It SUBMIT ANSWER Viewing Saved Work Revert to Last Response
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