At what point on the curve 3x^2 + 2y = 8 does the tangent make an angle of 45 degrees with the x-axis.

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The point on the curve 3x^2 + 2y = 8 is required where the tangent makes an angle of 45 degrees with the x-axis.

The slope of the tangent is tan 45 = 1.

The slope is also the value of `dy/dx` at that point.

3x^2 + 2y = 8

`6x + 2*(dy/dx) = 0`

=> `dy/dx = -3x`

1 = -3x

=> `x = -1/3`

y = `(8 - 3/9)/2`

=> `23/6`

The point on the curve 3x^2 + 2y = 8 at which the tangent makes an angle of 45 degrees with the x-axis is` (-1/3, 23/6)`

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