2324 Find a function g(x) of the formg(x) = Ax2 + Bx + Cwhose graph contains the points

Chapter 7, Problem 23

(choose chapter or problem)

Find a function g(x) of the form

\(g(x)=A x^{2}+B x+C\)

whose graph contains the points \((m-\Delta x, f(m-\Delta x))\), \((m, f(m))\), and \((m+\Delta x, f(m+\Delta x))\), for the given function f(x) and the given values of m and \(\Delta x\). Then verify Formula (11):

\(\int_{m-\Delta x}^{m+\Delta x} g(x) d x=\frac{\Delta x}{3}\left[Y_{0}+4 Y_{1}+Y_{2}\right]\)

where \(Y_{0}=f(m-\Delta x), Y_{1}=f(m), \text { and } Y_{2}=f(m+\Delta x)\).

\(f(x)=\frac{1}{x} ; m=3, \Delta x=1\)

Equation Transcription:

Text Transcription:

g(x)=Ax^2 +Bx+C

(m-delta x, f(m-delta x))

(m, f(m))

(m+delta x, f(m+ delta x))

delta x

integral _m-delta x ^m+delta x  g(x)dx=delta x/3  [Y_0 +4Y_1 +Y_2 ]

Y_0=f(m-delta x), Y_1 =f(m), and Y_2 =f(m+delta x)

f(x)=1/x ; m=3, delta x=1