# math

posted by .

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

• math -

4 y = 3 x + 0
y = (3/4) x
slope = m = 3/4

y = x^3 + k
dy/dx = slope = 3 x^2
so
3 x^2 = 3/4
x^2 = 1/4
x = 1/2 (-1/2 is not in first quadrant)
then
y = (1/2)^3 + k
y = 1/8 + k and y = 3x/4
so
3 x/4 = 1/8 + k
but x = 1/2
3/8 = 1/8 + k
k = 2/8 = 1/4

## Similar Questions

1. ### calculus

Consider line segments which are tangent to a point on the right half (x>0) of the curve y = x^2 + 1 and connect the tangent point to the x-axis. If the tangent point is close to the y-axis, the line segment is long. If the tangent …
2. ### calculus

If a tangent line is drawn to the parabola y = 3 - x^2 at any point on the curve in the first quadrant, a triangle is formed with the axes. At what point on the curve should the tangent be drawn to form a triangle of least are?
3. ### Calculus

If a tangent line is drawn to the parabola y = 3 - x^2 at any point on the curve in the first quadrant, a triangle is formed with the axes. At what point on the curve should the tangent be drawn to form a triangle of least area?
4. ### Calculus

Consider line segments which are tangent to a point on the right half (x>0) of the curve y = x^2+7 and connect the tangent point to the x-axis. If the tangent point is close to the y-axis, the line segment is long. If the tangent …
5. ### Calculus

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
6. ### calculus

Find the point on the curve y =2/3 〖√(18-x^2 )〗 (first quadrant) where a tangent line may be drawn so that the area of the triangle formed by the tangent line and the coordinate axes is a minimum.
7. ### Calculus

Find the area of the largest rectangle cut from the first quadrant by a line tangent to the curve y=e^(-x^2)
8. ### Calculus AB

Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x-1)e^x. For which value of x is the slope of the tangent line to f positive?