noe4geskirstc noe4geskirstc

04-08-2016
Mathematics

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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?

Respuesta :

08-08-2016

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

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