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 ) = x 2 − x
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 ) = x 2 − x
Solution Summary: The author illustrates the graph of the function f(x)=x-2-x.
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.
Find an equation for the tangent line to y = g(x) at the
point (2, g(2)). Write your result in point-slope form.
Submit
On the axes provided, sketch the tangent line to the
function g(x) at the point (2, g(2)).
-2
6
Write an equation of the tangent line to the graph of y = f(x) at the point on the graph where x has the indicated value.
12)
f(x) =
-10x2-3
-4x - 3
A) y=x+1
.x = 0
y=-x-1
B)
c) y = -x + 1
D) y=-. 1
University Calculus: Early Transcendentals (3rd Edition)
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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