Question

Let a>0 & b>0 be two positive numbers and consider the function f(x) = x^a+x^−b. Find the positive value of x where f(x) achieves its minimum value.

a. x=1

b. x=a/b

c. x=(b/a)^1/a+b

d. x=(ab)^a+b

e. x=(a+b)^ab

f. x=(b/a)^a+b

Answer #1

Given, where

Differentiate with respect to ,

For critical points,

To find minimum value, take second derivative of function and plug critical points

, has minimum value.

**Hence, Option c is correct.**

Consider the piecewise defined function
f(x) = xa− xb if 0<x<1. and
f(x) = lnxc if x≥1.
where a, b, c are positive numbers chosen in such a way that
f(x) is differentiable for all 0<x<∞. What can be said about
a, b, and c?

1. Consider the following optimization problem. Find two
positive numbers x and y whose sum is 50 and whose product is
maximal. Which of the following is the objective function?
A. xy=50
B. f(x,y)=xy
C. x+y=50
D. f(x,y)=x+y
2. Consider the same optimization problem. Find two positive
numbers x and y whose sum is 50 and whose product is maximal. Which
of the following is the constraint equation?
A. xy=50
B. f(x,y)=xy
C. x+y=50
D. f(x,y)=x+y
3. Consider the same...

If a and b are positive numbers, find the absolute maximum value
of the function f(x) = (x^b) (2-x)^a on the interval [0,2]. Your
final answer may depend on a and b.

let the density function of x be f(x) = e^−x, x>0, find of
the density function of Z = e^-x

Let F(x) = 1 − e −2x for x > 0 and F(x) = 0 for x ≤ 0. Is
F(x) a distribution function? Explain your answer. If it is a
distribution function, find its density function.

Consider the function f(x) = (8x^3-4x)^3
(a) Find the derivative
(b) Find critical numbers of f. (Hint there are 5 critical
numbers) Round your answers to three decimals.
(c) Fill out the sign chart for the derivative below. Please
label the axis as appropriate for your critical numbers.
(d) What are the relative max(es) and min() of f?

If a and b are positive numbers, find the maximum value of
f(x)=xa(5−x)b on the interval 0≤x≤5.

Consider the function below. y=f(x)= x/x^2+x+1
Find all critical numbers of (f), if any.
Find interval(s) on which f is decreasing
Final all local maximum/minimum points of f.

Let f be a function of two variables that has
continuous partial derivatives and consider the points
A(1, 1),
B(7, 1),
C(1, 13),
D(9, 16).
The directional derivative of f at A in the
direction of the vector
AB is 9 and the directional derivative at A in
the direction of
AC is 2. Find the directional derivative of f
at A in the direction of the vector
AD. (Round your answer to two decimal places.)

Let X be a random variable with probability density function
f(x) = { λe^(−λx) 0 ≤ x < ∞
0 otherwise } for some λ > 0.
a. Compute the cumulative distribution function F(x), where F(x)
= Prob(X < x) viewed as a function of x.
b. The α-percentile of a random variable is the number mα such
that F(mα) = α, where α ∈ (0, 1). Compute the α-percentile of the
random variable X. The value of mα will...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 seconds ago

asked 2 minutes ago

asked 9 minutes ago

asked 10 minutes ago

asked 16 minutes ago

asked 39 minutes ago

asked 52 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago