Posted by **krishna** on Friday, October 14, 2011 at 1:54pm.

if the line 3x-4y=0 is tangent in hte 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!

## Answer This Question

## Related Questions

- Calculus - Tangent Line - Hi, im having problems with the following problem. The...
- calculus - Find the point on the curve y =2/3 〖√(18-x^2 )〗 (...
- math - f(x) = 4e^-1x +13x +5 at (0,9) 1. All steps for finding the first ...
- Calculus - Find the area of the largest rectangle cut from the first quadrant by...
- Calculus - If F(x)=x^3−7x+5, use the limit definition of the derivative to...
- Calculus - Please help this is due tomorrow and I dont know how to Ive missed a ...
- Calculus - If the line 3x-4y=0 is tangent in the first quadrant to the curve y=x...
- Calculus - Consider the curve given by y^2 = 2+xy (a) show that dy/dx= y/(2y-x...
- AP Calc - Find the point on the curve x=4y-y^2 where the tangent to the curve is...
- Math - Find the point on the curve x=4y-y^2 where the tangent to the curve is a ...

More Related Questions