Question

1) a) Find the linearization of: f(x) = ^{3}/x (cube
root of x) at a = 8. Use it to approximate ^{3}/8.5 (cube
root of 8.5).

b) Find the absolute maximum and minimum values of f(x) = xe^-x (xe to the power of negative x) on the interval -1<x<1 (x is greater than or equal to -1 but less than or equal to 1)

Answer #1

(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...

Find the absolute maximum and absolute minimum values of f on
the given interval.
f(x) = xe-x^2/128, [-3,16]

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 absolute minimum values of f on
the given interval: x^4-8x^2+8 [-3, 4]
Absolute minimum:
Absolute maximum:

.
Consider the following. f (x) = x^5 − x^3+5 , − 1 ≤ x ≤ 1
(a) Use the graph to find the absolute maximum and minimum
values of the function to two decimal places.
(b) Use calculus to find the exact maximum and minimum
values

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 absolute minimum values of f on
the given interval. f(x)= ln(x^2+x+1), [-1,1]

Let f(x)=4x(^3)-9x(^2)+6x-1 Find:
a.) absolute minimum of f(x) on the interval [0,1].
b.) absolute maximum of f(x) on the interval [0,1].

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.

Let f(x) = x^3 + x - 4
a. Show that f(x) has a root on the interval [1,4]
b. Find the first three iterations of the bisection method on f
on this interval
c. Find a bound for the number of iterations needed of bisection
to approximate the root to within 10^-4

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