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10-03-2017
Mathematics

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

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10-03-2017

find the slope

3x-4y=0
3x=4y
y=3/4x
slope=3/4

take derivitive of y=x^3+k
y=3x^2

that is slope at mystery point
3x^2=3/4
x^2=1/4
x=1/2
input
y=3/4x
y=3/8
so

3/8=(1/2)^3+k
3/8=1/8+k
2/8=k
1/4=k

k=1/4

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