61. Find the points on the graph of y2 = x³ – 3x +1 (Figure 10) where the tangent line is horizontal. (a) First show that 2yy' = 3x² – 3, where y' = dy/dx. (b) Do not solve for y'. Rather, set y' = 0 and solve for x. This yields two values of x where the slope may be zero. (c) Show that the positive value of x does not correspond to a point on the graph. (d) The negative value corresponds to the two points on the graph where the tangent line is horizontal. Find their coordinates. FIGURE 10 Graph of y² = x – 3x +1.

61. Find the points on the graph of y2 = x³ – 3x +1 (Figure 10) where the tangent line is horizontal. (a) First show that 2yy' = 3x² – 3, where y' = dy/dx. (b) Do not solve for y'. Rather, set y' = 0 and solve for x. This yields two values of x where the slope may be zero. (c) Show that the positive value of x does not correspond to a point on the graph. (d) The negative value corresponds to the two points on the graph where the tangent line is horizontal. Find their coordinates. FIGURE 10 Graph of y² = x – 3x +1.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

See similar textbooks

Similar questions

If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.
Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
Find the slope of the line tangent to the curve x + sin(y-π) = 2x3 + ey at thr point (-1,0).
4. Find the equation of the line that is tangent to y = 2x + sin x + cos x at x = 0.
5. Find the equation of the line that is tangent to y = ln x at x = 1.
Find the slope of the tangent to the curve y=(cos 3x)/( 2-ln(2x+1) ) at x=0
The slope of the tangent line to the curve y = 4/x at the point (3, 4/3) is: Must be written in y = mx + b form
Determine the slope of the tangent line to the curve y= In x^2 at x = e^2
Find the equation of a curve whose third derivative at any point (x,y) is always equal to 6 and which has a critical point at (0,-2) and which is tangent to the line 3x+y+3=0 at x=-1.
Find the slope of the line tangent to the curve y = cos2 x at the point(−π/3 , 1/4)
Find the points on the graph of y = ex + e-2x where the tangent line is horizontal.