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(:

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