Posted by Britt on Sunday, December 9, 2007 at 6:41pm.
Find the equation of a tangent line of a graph pf y=x^2+4lnx, which is parallel to y=6x-3?
I know parallel lines have the same slope so the slope is 6 but I do not know how to find the b value.
- Calc - Damon, Sunday, December 9, 2007 at 6:47pm
Well you need to find where on that nasty function the slope is 6. Then at that (x,y) you write the y = 6 x + b that goes through that point.
- Calc - Britt, Sunday, December 9, 2007 at 6:50pm
how do I do this?
- Calc - Damon, Sunday, December 9, 2007 at 6:54pm
y = x^2 + 4 ln x
dy/dx = slope = 2 x +4/x
when is that slope 6?
6 = 2 x + 4/x
I get at x = 1 and at x = 2
well 1 is easy because ln 1 = 0. It just said "a" tangent line, not all tangent lines.
then y = 1
so I am going to use (1,1)
- Calc - Reiny, Sunday, December 9, 2007 at 6:55pm
actually it's not so bad
the derivative of your function is
2x + 4/x
setting this equal to 6 gave me a quadratic which factored nicely and had roots of
x = 1 or x=2
if x=1 then y = 1+4ln1
so one case is m=6, point (1,1)
x=2, then y = 4 + 4ln2
so m=6, point (2,4+4ln2)
- Calc - Damon, Sunday, December 9, 2007 at 6:55pm
All set now?
- Calc - Damon, Sunday, December 9, 2007 at 7:02pm
multiply both sides by x
6 x = 2 x^2 + 4
2 x^2 - 6 x + 4 = 0
1 x^2 - 3 x + 2 = 0
(x-1)(x-2) = 0
x = 1
x = 2 are solutions.
I used 1 so the point I could take was (1,1)
Answer This Question
More Related Questions
- HELP WITH ALGEBRA!! - 6. What happens to the graph of the line y = 3x -2 when ...
- math,correction - The question asks: Find the slope of any ilne parallel to the ...
- Algebra - 'L' has y-intercept (0,-3) and is parallel to the line with equation y...
- Algebra 1 - 1. Which line is the flattest (or is less steep)? Why? y = 5x -6 y...
- MATH! - What type of lines have a slope of zero? Write the equation of a line ...
- Algebra - I'm suppose to write an equation with the following information: Line ...
- Math - 1) What is the slope of a line that is parallel to y = 2? 2) What is the...
- algebra - identify the equation of the line through (-1,-4) and parallel to y=-...
- Pre-Algebra - Please let me know if I figured these out correctly. Directions: ...
- ALgebra 1 - 4. Write the equation of a line whose slope is 6 and whose y ...