Let . (i) Prepare a table of values of for integral in the interval . (ii) Plot the…
MATHEMATICS · Subjective · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions
Problem
Let f(x)=x3−4x.
(i) Prepare a table of values of f(x) for integral x in the interval −4≤x≤4.
(ii) Plot the corresponding points, select an appropriate uniform scale, and sketch the graph of y=f(x) as a smooth curve.
(iii) Using your graph, estimate the coordinates of the turning points of the curve correct to one decimal place.
(iv) Determine, from the graph, the number of real roots of f(x)=0 and write their approximate values.
(v) State the intervals of x (within the plotted window) for which f(x) is positive and for which it is negative.