For what values of a and b is the line 2x + y = b tangent to the parabola y = ax2 when x = 3?

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Mathematics

16 October, 10:40

For what values of a and b is the line 2x + y = b tangent to the parabola y = ax2 when x = 3?

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Odie · Answer 1

Y=ax^2

Differentiate both sides with respect to x, we have y'=2ax

Put x=3, we have y'=6a

Hence the slope of 2x+y=b is 6a, then a=-1/3

y = (-1/3) (3^2) = - 3

Put (3,-3) into the line,

b=6-3

Hence a=-1/3, b=3