Posted by Travis on Friday, September 21, 2012 at 3:59pm.
a) Sketch a curve whose slope is always positive and increasing.
b) Sketch a curve whose slope is always positive and decreasing.
c) Give equations for curves with these properties.
So for a, I drew a positive slope that was concave up. And for b, I drew a slope that was concave down. I drew both of these slopes going in a upward/right direction. Did I do that correctly? Also, I'm not sure how an equation should look for this? Thanks!

calculus  Steve, Friday, September 21, 2012 at 4:12pm
(a) y = e^x, since y'' = y' = e^x (both positive)
(b) y = e^x, since
y' = e^x positive
y'' = e^x negative
y = arctan(x) also fits here, since
y' = 1/(1+x^2) positive
y'' = 2x/(1+x^2)^2 negative
So the curve can change from concave up to concave down and still have decreasing slope
Answer This Question
Related Questions
 12th Grade Calculus  1. a.) Find an equation for the line perpendicular to the ...
 Math  Find 2 tangent line equations to the curve y=x^3+x at the points where ...
 calculus  1. Given the curve a. Find an expression for the slope of the curve ...
 slope  Find the slope of the line passing through the given points using the ...
 calculus  use the methods of this section to sketch the curve. y=x^33a^2x+2a^3...
 Calculus  Find the intervals on which y=1/(x^2+1)^2 is increasing and ...
 Calculus  The slope of the tangent to the curve (y^3)x+(y^2)x^2=6 at (1.2) is...
 Calculus  Find the equation of the curve passing through P (1,2) whose slope is...
 Math  Which of the following is TRUE about the line through the points (–1, 4) ...
 calculus  Describe the slope of the tangent line to the curve defined by x 2 + ...
More Related Questions