2. The function f (x) is given by f (x) =x² – 3x² + 3x, for –1

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter9: Quadratic Functions And Equations
Section9.9: Combining Functions
Problem 59PFA
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2. The function f (x) is given by f (x) =x² – 3x² + 3x, for –1<x<3.
(a) Differentiate f (x) with respect to x.
(b) Complete the table below.
-1
1
2
3
S(x)
S'(x) | 12
2
9
12
(c)
Use the information in your table to sketch the graph of f (x).
(d)
Write down the gradient of the tangent to the curve at the point (3, 9).
(e)
Write down the equation of the normal at the point (3, 9).
Transcribed Image Text:2. The function f (x) is given by f (x) =x² – 3x² + 3x, for –1<x<3. (a) Differentiate f (x) with respect to x. (b) Complete the table below. -1 1 2 3 S(x) S'(x) | 12 2 9 12 (c) Use the information in your table to sketch the graph of f (x). (d) Write down the gradient of the tangent to the curve at the point (3, 9). (e) Write down the equation of the normal at the point (3, 9).
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