Posted by krishna on Friday, October 14, 2011 at 1:54pm.
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
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.
thanks so much!
Related Questions
Calculus - If the line 3x-4y=0 is tangent in the first quadrant to the curve y=x...
math - If the line 3x-4y = 0 is tangent in the first quadrant to the curve y = x...
Ap calculus - Find the equation of the tangent line to the curve g(X)= 2cos(2X...
Calculus - Please help this is due tomorrow and I dont know how to Ive missed a ...
Calculus - the curve: (x)(y^2)-(x^3)(y)=6 (dy/dx)=(3(x^2)y-(y^2))/(2xy-(x^3)) a...
Calculus - If a tangent line is drawn to the parabola y = 3 - x^2 at any point ...
calculus - If a tangent line is drawn to the parabola y = 3 - x^2 at any point ...
Calculus - Damon - Find the line which passes through the point (0, 1/4) and is ...
Calculus - Consider the curve y^2+xy+x^2=15. What is dy/dx? Find the two points ...
last calc question, i promise! - given the curve x + xy + 2y^2 = 6... a. find an...
For Further Reading
