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
k is y_intercept of tangent line

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

tangent line passes through point (-2,-1)

k = x+y

k = -2 -1

k = -3