Pages • 1
Ib Math Hl Ia, Zeros of Cubic FunctionsMathematics IB Higher Level Portfolio (Internal Assessment):Zeros of Cubic FunctionsBrendan LeeMarch 2010Q1: Consider the Cubic equation:〖f(x)=2x〗^3+〖6x〗^2-4.5x-13.5:The graph is shown here:Graphed on GCalc 3.0The zeros of this equation are:x=-1.5x=1.5This can be proved using the remainder theorem:f(-3)=0f(-1.5)=0f(1.5)=2(3.375)+6(2.25)-6.75—13.5f(1.5)=0Equations of tangent lines at average of two roots:Roots -1.5 and -3:Average: (-1.5+(-3))/2=-2.25y≈-4.2Slope at.