For the function, find the points on the graph at which the tangent line is horizontal. If none exist, state that fact. f(x) = 2x2 - 3x +3

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.6: Solving Quadratic Equations By Using The Quadratic Formula
Problem 64PFA
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Find the points on the graph at which the tangent line is horizontal

f(x)=2x^2-3x+3

For the function, find the points on the graph at which the tangent line is horizontal. If none exist, state that fact.
f(x) = 2x2 - 3x +3
Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. The point(s) at which the tangent line is horizontal is (are)
(Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)
O B. There are no points on the graph where the tangent line is horizontal.
OC. The tangent line is horizontal at all points of the graph.
Transcribed Image Text:For the function, find the points on the graph at which the tangent line is horizontal. If none exist, state that fact. f(x) = 2x2 - 3x +3 Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The point(s) at which the tangent line is horizontal is (are) (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) O B. There are no points on the graph where the tangent line is horizontal. OC. The tangent line is horizontal at all points of the graph.
Expert Solution
Step 1

For horizontal tangent line 

f'(x) =  0

Which means slope is zero .

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