posted by .

Determine the absolute extrema of each function on the given interval. Illustrate your results by
sketching the graph of each function.

f(x) = (x − 1)^2 , 0 ≤ x ≤ 2

clearly a simple parabola

f ' (x) = 2(1-x) = 0 for a max/min
x=1
f(1) = (1-1)^2 = 0

endpoints:
f(0) = (-1)^2 = 1
f(2) = (162 = 1

parabola opens up, so the minimum is 0 when x = 1

or
(the vertex is (1,0) )

You have posted several of these rather straightforward problems. What is it exactly that you are having difficulties with ?

## Similar Questions

1. ### Calculus

If m ≤ f(x) ≤ M for a ≤ x ≤ b, where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then m(b − a) ≤ b f(x) dx a≤ M(b − a). Use this property to estimate …
2. ### Calculus

If m ≤ f(x) ≤ M for a ≤ x ≤ b, where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then m(b − a) ≤ b f(x) dx a≤ M(b − a). Use this property to estimate …

Determine the absolute extrema of each function on the given interval. Illustrate your results by sketching the graph of each function. a)  =  − 4 + 3 , 0 ≤  ≤ 3 b)  =  − 1 , 0 ≤  ≤ …

Determine the absolute extrema of each function on the given interval. Illustrate your results by sketching the graph of each function. a) f(x) = x^2 − 4x + 3 , 0 ≤ x ≤ 3 b) f(x) = (x − 1)^2 …

Determine the maximum and minimum of each function on the given interval. a)  = 2x^3 − 9x^2 ,−2 ≤ x ≤ 4 b)  = 12x − x^3 ,  x∈ [−3,5]
6. ### calculus

Determine the maximum and minimum of each function on the given interval. a)  = 2x^3 − 9x^2 ,−2 ≤ x ≤ 4 b)  = 12x − x^3 ,  x∈ [−3,5]