Thursday

July 31, 2014

July 31, 2014

Posted by **Rudy** on Wednesday, December 5, 2012 at 1:29am.

a) Find dy/dx. Simplify your answer

b) Find the coordinates of any points on the graph of y where the tangent line is horizontal. Show your work.

c) Are there any points on the graph of y where the tangent line is parallel to the line y=x+7? Explain your answers.

- Calculus -
**Steve**, Wednesday, December 5, 2012 at 11:37amy' = (x^2+6x+5)/(x+3)^2 = (x+1)(x+5)/(x+3)^2

or, you could say y = x-3+4/(x+3), so

y' = 1 - 4/(x+3)^2

so, where is y'=0? x = -1 or -5

where is y'=1? nowhere, since 1-4/(x+3)^2 < 1 for all x. Note that y has a slant asymptote with slope=1.

**Related Questions**

calculus - 4. Given the function f defined by f(x) = cos2x for -π≤ x...

calculus - let f be the function f(x) = x^3 + 3x^2 - x + 2 a. the tangent to the...

Calculus - Use the given equation to answer the following questions. (Enter your...

Calculus - 55. Find an equation of the tangent line to the graph of f(x) =x^3 - ...

math - Consider the function f(x)= -cos3x -4sin3x. (a)Find the equation of the ...

math - help me ..... Consider the function f(x)= -cos3x -4sin3x. (a)Find the ...

math - help me ..... Consider the function f(x)= -cos3x -4sin3x. (a)Find the ...

math - weloo. Consider the function f(x)= -cos3x -4sin3x. (a)Find the equation ...

calculous - 3.Given the function f defined by f(x)=2x^3-3x^2-12x+20 a.Find the ...

Derivative Calculus - I just need my answers checked. 1) Find the derivative. f(...