Question

(a) Find the maximum and minimum values of f(x) = 3x 3 − x on the closed interval [0, 1] by the following steps:

i. Observe that f(x) is a polynomial, so it is continuous on the interval [0, 1].

ii. Compute the derivative f 0 (x), and show that it is equal to 0 at x = 1 3 and x = − 1 3 .

iii. Conclude that x = 1 3 is the only critical number in the interval [0, 1].

iv. Compute the values f(0), f(1), and f( 1 3 ); and indicate the maximum and minimum values of f(x) on [0, 1].

(b) Find the absolute maximum and minimum values of F(x) = x + 9 x on the closed interval [1, 20]. HINT: Use the same steps as the previous problem

Answer #1

Find the absolute maximum and absolute minimum values of f on
the given interval. f(x) = 3x^2 − 18x + 8, [0, 8] absolute minimum
value.

Find the absolute maximum and minimum values of f(x)=
−x^3−3x^2+4x+3, if any, over the interval
(−∞,+∞)(−∞,+∞).
I know it doesn't have absolute maxima and minima but where do
they occur? In other words x= ? for the maxima and minima?

1. The absolute maximum value of f(x) = x 3 − 3x 2 + 12 on the
interval [−2, 4] occurs at x =? Show your work.
2.t. Let f(x) = sin x + cos2 x. Find the absolute maximum, and
absolute minimum value of f on [0, π]. Show your work.
Absolute maximum:
Absolute minimum:
3.Let f(x) = x √ (x − 2). The critical numbers of f are_______.
Show your work.

find the absolute maximum and absolute minimum values of f on
the given closed interval
f(x)=5-x^2
[-3,1]

Let f(x) = x 1/2 (3−x). Find the absolute maximum and absolute
minimum values of the f(x) on the interval [1, 3].

Find the absolute maximum and minimum values of each function
over the indicated interval, and indicate the x-values at which
they occur.
f(x) = 3x^3 - 3x^2 - 3x + 7 ; [-1 , 0]
The absolute maximum value is _ at x = _
(Use a comma to separate answers as needed. Type an integer or
a fraction.)

Find the absolute maximum and absolute minimum values of f on
the given interval. f(x) = x4 − 2x2 + 1, [−2, 3] absolute minimum
Incorrect: Your answer is incorrect. absolute maximum Incorrect:
Your answer is incorrect.

Find the absolute maximum and absolute minimum values (if they
exist) of f(x) = ln x/x on the interval (0, ∞).

Find the absolute minimum and absolute maximum of
f(x,y)=10−3x+8y
on the closed triangular region with vertices (0,0),(8,0) and
(8,12).
List the minimum/maximum values as well as the point(s) at which
they occur. If a min or max occurs at multiple points separate the
points with commas.

find the absolute maximum and absolute minimum values of f on the
given interval
f(x) = x^4-2x^2+1 [-2,3]

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 2 minutes ago

asked 3 minutes ago

asked 3 minutes ago

asked 3 minutes ago

asked 3 minutes ago

asked 4 minutes ago

asked 5 minutes ago

asked 5 minutes ago

asked 6 minutes ago

asked 8 minutes ago

asked 9 minutes ago