1. Consider the following graph of f(x) =-(*-5x' +3x+1)052.545a. List any x-values at which f(x) is not differentiable: f(x) is differentiable everywhere because it is continuousb. Sketch the tangent line to the curve at x = =1. Shown in my work below.c. Given that f' (x) == (3x² – 10x + 3), find f'(-1). 8d. Find the slope of the tangent line at x = -1. 8e. At what ordered pair location does the tangent line make contact with f (x)?f. Give the equation of the tangent line you drew in part b.g. Sketch the tangent line to the curve at x = 1.h. Use the derivative to find the slope of the tangent line at x = 1.i. At what ordered pair location does the tangent line make contact with f (x)?.j. Give the equation of the tangent line you drew in part g.k. Are there any locations at which f (x) would have tangent lines that have a slope of 0? If so, draw tangent lines to thecurve at that/those locations.

Answered: 1. Consider the following graph of f(x)…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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1. Consider the following graph of f(x) =-
(*-5x' +3x+1)
05
2.5
45
a. List any x-values at which f(x) is not differentiable: f(x) is differentiable everywhere because it is continuous
b. Sketch the tangent line to the curve at x = =1. Shown in my work below.
c. Given that f' (x) == (3x² – 10x + 3), find f'(-1). 8
d. Find the slope of the tangent line at x = -1. 8
e. At what ordered pair location does the tangent line make contact with f (x)?
f. Give the equation of the tangent line you drew in part b.
g. Sketch the tangent line to the curve at x = 1.
h. Use the derivative to find the slope of the tangent line at x = 1.
i. At what ordered pair location does the tangent line make contact with f (x)?.
j. Give the equation of the tangent line you drew in part g.
k. Are there any locations at which f (x) would have tangent lines that have a slope of 0? If so, draw tangent lines to the
curve at that/those locations.

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$(a) n o X - v a l u e s f (x) i s d i f f e r e n t i a b l e e v e r y w h e r e \sin c e i t i s a s m o o t h c u r v e$

$(b) f (x) = \frac{1}{2} (x^{3} - 5 x^{2} + 3 x + 1) d i f f w . r . t x f' (x) = \frac{1}{2} (3 x^{2} - 10 x + 3) f' (- 1) = \frac{1}{2} (3 {(- 1)}^{2} - 10 (- 1) + 3) f' (- 1) = \frac{1}{2} (3 + 10 + 3) = \frac{1}{2} \times 16 = 8 f' (- 1) = 8 s o s l o p e o f \tan g e n t a t x = - 1 i s m = 8 f (- 1) = \frac{1}{2} ({(- 1)}^{3} - 5 {(- 1)}^{2} + 3 (- 1) + 1) = \frac{1}{2} (- 8) = - 4 f (- 1) = - 4 h e n c e p o i n t o f c o n t a c t i s (- 1, - 4) e q u a t i o n o f \tan g e n t i s y + 4 = m (x + 1) \Rightarrow y + 4 = 8 (x + 1) \Rightarrow y = 8 x + 4$