Calculus Question

Question

Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (If an answer does not exist, enter DNE.)

f(x) = 6 −

x

absolute maximum

Answer 1

y = 6- sqr(x) is the bottom half of a leftward opening parabola with vertex (0,6) and 6 = the absolute maximum There is no minimum, local or absolute. range is y< 6, domain is x>0

y-6 = sqr(x)

x = (y-6)^2 with x>0

the bottom half of the parabola x= y^2 -36y +36

y intercept = 6, the point (0,6)

x intercept = 36, the point (36, 0)

f'(x) = -1/sqrx which never = 0, although it approaches zero as x approaches infinity. There is no local minimum