Posted by **Rudy** on Monday, October 29, 2012 at 2:32am.

If the line 3x-4y=0 is tangent in the first quadrant to the curve y=x^3+k, then k is

a: 1/2

b: 1/4

c: 0

d: -1/8

e: -1/2

- Calculus -
**Reiny**, Monday, October 29, 2012 at 9:00am
if y = x^3 + k

dy/dx = 3x^2 , which of course is the slope of the tangent

but the slope of the given line is 3/4 , so ...

3x^2 = 3/4

x^2 = 1/4

x = ± 1/2 , but since we are restricted to the first quad,

x = 1/2

if x=1/2, 3(1/2) - 4y = 0

y = 3/8

The point of contact of the tangent is (1/2 , 3/8)

so in the cubic ...

3/8 = (1/8) + k

k = 3/8-1/8 = 1/4

- Calculus -
**Rudy**, Tuesday, October 30, 2012 at 2:06am
Thank youu(:

## Answer This Question

## Related Questions

- calculus - Find the point on the curve y =2/3 〖√(18-x^2 )〗 (...
- 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 ...
- math - If the line 3x-4y = 0 is tangent in the first quadrant to the curve y = x...
- Calculus - Consider line segments which are tangent to a point on the right ...
- Calculus - I am doing the AP calculus review, these are the questions I have no ...
- calculus - Consider line segments which are tangent to a point on the right half...
- calculus--please helpp - if the line 3x-4y=0 is tangent in hte first quadrant to...
- calculus - Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show ...
- Calculus - A line in the first quadrant is tangent to the graph of y=1/x^2. How ...

More Related Questions