Sunday

December 21, 2014

December 21, 2014

Posted by **Travis** on Friday, September 21, 2012 at 3:59pm.

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 ...

calculus - use the methods of this section to sketch the curve. y=x^3-3a^2x+2a^3...

Calculus - a) Estimate the area under the graph of f(x)=7+4x^2 from x=-1 to x=2...

calculus - 1. Given the curve a. Find an expression for the slope of the curve ...

Calculus - Find the equation of the curve passing through P (1,2) whose slope is...

Business Statistics - In each case, sketch the two speciﬁed normal curves...

chemistry 12 - hey i was wondering, i have this question: Sketch a pH curve for ...

Calculus - Find the intervals on which y=1/(x^2+1)^2 is increasing and ...

maths - Find the equation of the curve through (4,2) whose tangent (for x > 0...

Chemistry - I really don't get pH curves. I have to sketch a pH curve for the ...