Problems 87-94 require the following discussion of a secant line. The slope of the secant line containing the two points ( x , f ( x ) ) and ( x + h , f ( x + h ) ) on the graph of a function y = f ( x ) may be given as In calculus, this expression is called the difference quotient of f (a) Express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer. (b) Find m sec for h = 0.5 , 0.1, and 0.01 at x = 1 . What value does m sec approach as h approaches 0? (c) Find an equation for the secant line at x = 1 with h = 0 .01 . (d) Use a graphing utility to graph f and the secant line found in part (c) in the same viewing window. 93. f ( x ) = 1 x
Problems 87-94 require the following discussion of a secant line. The slope of the secant line containing the two points ( x , f ( x ) ) and ( x + h , f ( x + h ) ) on the graph of a function y = f ( x ) may be given as In calculus, this expression is called the difference quotient of f (a) Express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer. (b) Find m sec for h = 0.5 , 0.1, and 0.01 at x = 1 . What value does m sec approach as h approaches 0? (c) Find an equation for the secant line at x = 1 with h = 0 .01 . (d) Use a graphing utility to graph f and the secant line found in part (c) in the same viewing window. 93. f ( x ) = 1 x
Solution Summary: The author explains how the function f (x) = 1 x requires the discussion of a secant line.
Problems 87-94 require the following discussion of a secant line. The slope of the secant line containing the two points
and
on the graph of a function
may be given as
In calculus, this expression is called thedifference quotient of f
(a) Express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer.
(b) Find msec for
, 0.1, and 0.01 at
. What value does msec approach as h approaches 0?
(c) Find an equation for the secant line at
with
.
(d) Use a graphing utility to graph f and the secant line found in part (c) in the same viewing window.
Based on your observation, what is the relationship between the graph of the two functions? What are the values of the function given the values of x and value of b.
1. Can the graph of a function have more than one tangent at a given point? Explain by
giving an example and solution with derivatives.
2. Is there a fiunction whose graph doesa't have a tangent at some point? Explain by giving
an example and solution.
For items 3-5: Given a function fix) -x -5x +3
a. Find the slope of the line tangent to the graph of the fiunction at point (2,3)
b. Find the equation of the tangent line
C. Find the equation of the normal line
I wrote everything out on my paper here, but I need to know what I am doing wrong with linear function values using function notation. I am trying to understand but having a nervous breakdown. I did 10 problems on a practice quiz online and it keeps reading wrong. No matter if I carefully re-try with the same formulas.
Forms used: y-y1=m(x-x1)
M= y2-y1/x2-x1
Y=mx+b
I was supposed to write an equation for these problems.
If this seems confusing feel free to ignore lol
Calculus, Single Variable: Early Transcendentals (3rd Edition)
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