12) 2 1 -3₂ A)x=0, x=3 C) x = 3 x B) Function is differentiable at all points. D) x = 0 13

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.2: Polynomial Functions
Problem 96E: What is the purpose of the Intermediate Value Theorem?
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Find the derivative of the function using the limit definition of a derivative
(the limit as h approaches 0 of ( f(x + h) - f(x))/h)
and evaluate the derivative at the given x-value.
6) f(x)=2x2+x-3 at x = 4
8
7) f(x) = -x-4
8) f(x) =
Find an equation for the line tangent to the graph of the given function at the indicated point.
Use the limit definiton of a derivative to compute the slope of the tangent line.
36
x-3
A) y = - 36x + 72
at x = -1
9) f(x) = x3 - x² at (0, 0)
A) y = 1
12)
10) y=-10√√x+2 at x = 1
when x = 2
2
y
List the x-values in the graph at which the function is not differentiable.
11)
2
1
A) x = -2, x=0, x=2
C) x = 0
y
A) x=0, x= 3
C) x = 3
st
-2
B) y = 72x + 108
B) y = 3
C) y=-36x + 36
x
C) y = -2
D) y = - 36x
6)
D) y = 0
7)
10)
B) Function is differentiable at all points.
D) x = -2, x = 2
B) Function is differentiable at all points.
D) x = 0
8)
9)
11)
12)
Transcribed Image Text:Find the derivative of the function using the limit definition of a derivative (the limit as h approaches 0 of ( f(x + h) - f(x))/h) and evaluate the derivative at the given x-value. 6) f(x)=2x2+x-3 at x = 4 8 7) f(x) = -x-4 8) f(x) = Find an equation for the line tangent to the graph of the given function at the indicated point. Use the limit definiton of a derivative to compute the slope of the tangent line. 36 x-3 A) y = - 36x + 72 at x = -1 9) f(x) = x3 - x² at (0, 0) A) y = 1 12) 10) y=-10√√x+2 at x = 1 when x = 2 2 y List the x-values in the graph at which the function is not differentiable. 11) 2 1 A) x = -2, x=0, x=2 C) x = 0 y A) x=0, x= 3 C) x = 3 st -2 B) y = 72x + 108 B) y = 3 C) y=-36x + 36 x C) y = -2 D) y = - 36x 6) D) y = 0 7) 10) B) Function is differentiable at all points. D) x = -2, x = 2 B) Function is differentiable at all points. D) x = 0 8) 9) 11) 12)
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