What is the value of c if y = 3x - 4 is a tangent to y = 4x^2 - 3x + c.

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The line y = 3x - 4 is a tangent to y = 4x^2 - 3x + c. This is the case when y = 3x - 4 touches the curve defined by y = 4x^2 - 3x + c only at one point. For this y = 4x^2 - 3x + c = 3x - 4 should have only one solution.

4x^2 - 3x + c = 3x - 4

=> 4x^2 - 6x + c + 4 = 0

The quadratic equation ax^2 + bx + c = 0 has a common root if the determinant b^2 - 4ac' = 0.

Here, a = 4, b = -6 and c' = c + 4

b^2 - 4*a*c' = 0

=> 36 = 4*4*(c + 4)

=> c + 4 = 36/16 = 9/4

=> c = -7/4

The required value of c for which the line y = 3x - 4 is a tangent to y = 4x^2 - 3x + c is -7/4

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