Question

1. Find the absolute minimum and maximum value of f(x) = x4 − 18x 2 + 7 (in coordinate form) on [-1,4]

2. If f(x) = x3 − 6x 2 − 15x + 3 discuss whether there are any absolute minima or maxima on the interval (2,∞)

show work please

Answer 1

1)

we have

the behaviour of f'(x),

	x=-1	-1<x<0	x=0	0<x<3	x=3	3<x<4	x=4
sign	NA	+	0	-	0	+	NA
behaviour	minimum	increasing	maximum	decreasing	minimum	increasing	maximum

the minimum at x = -1,

the minimum at x = 3,

the maximum at x = 0,

the maximum at x = 4,

hence the absolute minimum is (3, -74) and the absolute maximum is (0, 7)

2)

the behaviour of f'(x),

	x=2	2<x<5	x=5	x>5
sign	NA	-	0	+
behaviour	maximum	decreasing	minimum	increasing

the minimum at x = 5,

the maximum at x = 2,

hence the absolute minimum is (5, -97) and the absolute maximum is (2, -43)