Question

in the xy-plane, the line x + y=k, where k is a constant, is tangent to the graph of y=x^2+3x+1. What is the value of k?

Answer 1

slope of tangent line = dy/dx = 2x + 3

2x + 3 = -1
x = -2
y = -2^2 + 3 (-2) + 1 = -1

Tangent line passed through point (-2 , 1)
k = x + y
k = -2 - 1
k = -3

hope this helps