Posted by krishna on Friday, October 14, 2011 at 1:54pm.
if the line 3x-4y=0 is tangent in the first quadrant to the curve y=x^3+k, find k.
all i know is that its related to finding a derivative and i m basically completely lost....can please someone provide me some help?????
calculus--please helpp - Steve, Friday, October 14, 2011 at 2:12pm
the derivative gives the slope of the tangent line to the curve, at any point (x,y)
The line 3x-4y=0 has slope= 3/4
At any point on the curve (x,x^3 + k) the slope of the tangent line is 3x^2
So, you want to find x where 3x^2 = 3/4
x = 1/2
so, now you have y = 1/2^3 + k = 1/8 + k
What point on the line has y = 1/8 + k?
3* 1/2 - 4(1/8 + k) = 0
3/2 - 1/2 - 4k = 0
4k = 1
k = 1/4
So, y = x^3 + 1/4
At x = 1/2, y = 1/8 + 1/4 = 3/8
Note that at the point (1/2 , 3/8) 3x-4y = 0
calculus--please helpp - Steve, Friday, October 14, 2011 at 3:06pm
Note on missing answer.
x can also be -1/2 if 3x^2 = 3/4
In that case, k = -1/4
and the point of tangency is (-1/2 , -3/8)
Note also, that if the line had been 3x-4y=1, the same line would have touched the curve at both points, with k=0.
calculus--please helpp - krishna, Saturday, October 15, 2011 at 10:09am
thanks so much!
calculus--please helpp - Anonymous, Friday, November 4, 2016 at 1:24pm
Answer This Question
More Related Questions
- Calculus AB - Could someone please help me with these tangent line problems? 1) ...
- calculus - what is the derivative? - Let f(x) = 2x^2 + 1 a. Find the derivative ...
- Calculus - Tangent Line - Hi, im having problems with the following problem. The...
- Calculus - Damon - Find the line which passes through the point (0, 1/4) and is ...
- calculus - Find the point on the curve y =2/3 〖√(18-x^2 )〗 (...
- Calculus - Please help this is due tomorrow and I don't know how to Ive missed a...
- Calculus Part 2 - y = tan(sqrtx) Find dy/dx. So I found it and I got the answer ...
- Calculus [finding slope of tangent line] - Find the slope of the tangent line to...
- Calculus questions..really need help, please! - 1) Find the value of the lim(x-&...
- math - f(x) = 4e^-1x +13x +5 at (0,9) 1. All steps for finding the first ...