MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Consider the function f(x)=x3−6x2+9x+1.
(i) Find f′(x).
(ii) Determine all critical points of f.
(iii) Divide the real line into appropriate intervals and find the interval(s) where f is increasing and where it is decreasing.
(iv) Hence obtain the coordinates of all local maxima and minima of the curve y=f(x).