The angle of intersection between the equation f(x) = 3x and g(x) = 4-x² is 45⁰
What is Angle of Intersection?
Angle of intersection between two curves is the acute angle between the tangents to the curves at the intersection point.
Here, f(x) = 3x
then slope of f(x), [tex]m_{1}[/tex] = 3
g(x) = 4 - x²
then slope of g(x) , [tex]m_{2}[/tex] = -2 at x = 1
Now, Angle of intersection, tan θ = [tex]\frac{m_{2}-m_{1} }{1+ m_{1}m_{2} }[/tex]
tan θ = (-2 - 3) / (1 + 3.(-2))
tan θ = -5 / -5
tan θ = 1
θ = 45⁰
Thus, The angle of intersection between the equation f(x) = 3x and g(x) = 4-x² is 45⁰.
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