a. a) Graph the function. b. b) Draw tangent lines to the graph at point whose x -coordinates are –2, 0, and 1. c. c) Find f ' ( x ) by determining lim x → 0 f ( x + h ) − f ( x ) h . d. d) Find f ' ( − 2 ) , f ' ( 0 , ) and f ' ( 1 ) . These slopes should match those of the lines you drew in part ( b ). f ( x ) = − 5 x 2 − 2 x + 7
a. a) Graph the function. b. b) Draw tangent lines to the graph at point whose x -coordinates are –2, 0, and 1. c. c) Find f ' ( x ) by determining lim x → 0 f ( x + h ) − f ( x ) h . d. d) Find f ' ( − 2 ) , f ' ( 0 , ) and f ' ( 1 ) . These slopes should match those of the lines you drew in part ( b ). f ( x ) = − 5 x 2 − 2 x + 7
Solution Summary: The author explains how to graph the function f(x) to obtain the corresponding values.
a) Graph the function f(x) = 2x² - 9x + 10.
b) Draw a tangent line to the graph at the point whose x-coordinate is 3.
c) Find f'(x) by determining lim
f(x +h)- f(x)
R
d) Find f'(3). This slope should match that of the line you drew in part (b).
a) Choose the correct graph of the function.
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b) Choose the correct graph of the tangent line.
Click to select your answer(s).
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5.
a) Identify f, f', and f' from the graph below.
b) Sketch the graph of the derivative in the blank box.
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c)
State where the function is not differentiable and explain why.
Prob. 6 (a) (10 point) Let f(x) = 2x² – 3. Find ƒ'(−2) using only the limit definition of
derivatives.
(b) (10 p.) If ƒ(x) = √√x + 6, find the derivative f'(c) at an arbitrary point c using only the
limit definition of derivatives.
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY