at a particular point of the curve y=x^2+k, the equation of the tangent is y=6x-7, find the value of the constant k?

Answer 1

Using the general formula for the tangent line at x = a, in this case it would be y = a² + k + 2a(x – a) = 6x – 7. Comparing the coefficients of x tells us a = 3, so the line becomes y = –9 + k + 6x = 6x – 7, Thus k = 2.