Consider the following function.1(-) = {16-, r<0-7r, r>0%3D(a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)(b) Find the open intervals on which the function is increasing or decreasing.Increasing:O (-∞, 0)O (-∞, 16)O (0, 0)O (16, o)Decreasing:O (-0, 0)O (-, 16)O (0, o)O (16, o)(c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.)relative maximum (x, y)relative minimum (x, y)(d) Use a graphing utility to confirm your results.

NOTE: Refresh your page if you can't see any equations. . the first function is

Consider the following function. s(2) = { 16 , <0 -7z, r>0 %3D (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.) X = (b) Find the open intervals on which the function is increasing or decreasing. Increasing: O (-∞, 0) O (-o, 16) O (0, o) O (16, o)

Consider the following function. s(2) = { 16 , <0 -7z, r>0 %3D (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.) X = (b) Find the open intervals on which the function is increasing or decreasing. Increasing: O (-∞, 0) O (-o, 16) O (0, o) O (16, o)

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

See similar textbooks

Related questions

Q: A ball thrown vertically downward from the top of a building at a velocity of 64 ft/sec hits the gro...

A: Projectile motion

Q: Determine whether the integral is convergent or divergent. The integral from negative infinity to 0,...

Q: x+tan x 4. lim X→0 sin x

Q: Show your complete solution.

A: Given that: 1. f(x)=3x2+2x2. f(x)=1x3. f(x)=8x-2

Q: u - 1 Find dy/dx, given y : and u =Vx + 2. u* + 1

A: We can find the derivative as below.

Q: Calculate by using integration by substitution, sec? V5 (4) tan 17 dx What was your substitution? u ...

A: For the following problem,

Q: Use implicit differentiation to find y' and then evaluate y' at (3,0). 9 eY =x2 -y? %3D y' =] y'l(3....

A: topic - implicit differentiation

Q: x+ 4x2-9x-36 y = 4x2+28х+48

Q: 1. Find an equation of the line that is tangent to the graph of f and parallel to the given line. 1 ...

A: Topic = Functions

Q: is Convergent Determine whether each those that are convergent. integral divergento Evah or In X

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

A: Series convergence and divergence

Q: cos x 3) 1+ sin x 6) [cosh vdv

Q: Find the equation(s) of the tangent line(s) at the point(s) on the graph of the equation y-xy- 12=0,...

A: Topic = Functions

Q: Find the slant asymptote with limits

A: Given function f(x)=(x-2)(x+2)(x+1)(x+3)(x+1)

Q: dx xVx2/3-7 XVX

A: An proper and improper integral is an definite integral. ∫1x2+a2dx = 1atan-1xa+C

Q: Find the vector equation of the line, L that passes through the points P (2, -2, 8) and Q (10, 8, 3)...

A: Given problem:- Find the vector equation of the line, L that passes through the points P (2, -2, 8) ...

Q: -dx. Evaluate ſ &-3)(x*-1) ,. х2-2х-3

Q: Use implicit differentiation to find y' for the equation below and then evaluate y' at the indicated...

Q: dy (8y – a²y) + x – xy² = 0 dx

Q: Express the repeating decimal as a fraction. 0.101010...

Q: Express the repeating decimal as a fraction. 0.904818181818... 0.904818181818...

A: Let x=0.904818181818... Multiply 1000 on both sides.

Q: A function f is differentiable at a number a.. A. ... if lim f(x) = f(a), f(z) – f(a) B. ... if lim ...

A: topic - condition for differentiable function

Q: Determine whether the equation defines y as a function of x. Please show all the detail steps of you...

Q: Evaluate the iterated integrals ∫1 0 ∫1 0 dxdy

A: Given query is to find the value of the integral.

Q: Identify the quadric surface each of the following equations represent and sketch its graph in a dra...

A: The objective is to Identify the quadric surface and sketch it's graph.

Q: 1. Revenue is calculated by multiplying the price of an item by the quantity sold: Revenue = Price •...

Q: 6x+5x-1 lim X--1 7x-2

A: Topic = Limits

Q: Let S(z) = {-3z? + 5z for z 0. 3z2-2 According to the definition of the derivative, to compute f'(0...

Q: 3. lim f(x) = -2, lim, f(x) = 2 and f(2) = 0 4. lim f(x) = +0, g, f(x) = -0

Q: b) Suppose that f(x) 1 if x is negative. Can ƒ be continuous at x = 0?

Q: Find x' for x(t) defined implicitly by x +tx+t° - 4 = 0 and then evaluate x' at the point (-2,-6). x...

A: We have to find the value of x' at point (-2, -6)

Q: (a) Find the point of intersection of the tangent lines to the curve r(e) = (5 sin(at), 6 sin(æt), 4...

A: Given: r(t) = ⟨ 5 sinπt , 6 sinπt , 4 cosπt ⟩ When t = 0 and t = 0.5

Q: x²dx x3+ 4

Q: It is possible for la + b| < ]ã|

A: topic- vetors

Q: A triangular lot, where all its three sides have the same length, is to contain a triangular buildin...

A: The figure is shown below: △ABC represents triangular lot.△DEF represents traingular building

Q: dx xVx2/3-7 XVX

A: Given that: ∫dxxx2/3-7

Q: Write your answer on a piece of paper with your name on it. Snap a picture, then upload your answer....

Q: Question Find far for f(, e tan(). Sorry, that's incorreci. Try again?

Q: Use the Simpson's Rule to approximate the given integral with n= 8. (Find Ss.) Round your answers to...

Q: 1. Revenue is calculated by multiplying the price of an item by the quantity sold: Revenue = Price •...

Q: Let f(x) = x' cos ( x-) and calculate ed S(x) dx by using integration by substitution. What was your...

Q: Write the first five terms of the sequence: 17 ln n n Determine whether the sequence converges, and ...

A: We will find the first five term of the sequence and also find the limit if given sequence is conver...

Q: Perform the indicated operation without the use of a calculator and express each answer in decimal n...

A: Topic = Algebra correct option = C

Q: 1. Use the following matrices to compute the indicated expression if it is defined. [ 3 A = 15 21 6 ...

Q: Use implicit differentiation to find y' and then evaluate y' at (-2,1). x In y + 6y = 3x ] y'l(-2.1)...

A: This question is related to differetiation. solve in step 2

Q: x(x²-x+2) dx is equal to 3

Q: The temperature T (in °C) at a location in the Northern Hemisphere depends on the longitude x, the l...

Q: Find lim (x,y,z)-(0,0,0) x²+y2+z4 xy+yz?+xz2 if it exists, or show that the limit does not exist.

Q: If x2+y?+z? = 9, dt dx dy = 7, find zp dt when (x, y, z) = (2,2,1). = 8, %3D %3D dt dz dt X when (x,...

A: Given x2+y2+z2=9dxdt=8, dydt=7

Q: 24. f(x, y) = In(x² + y)

Question

Consider the following function.
1(-) = {
16-, r<0
-7r, r>0
%3D
(a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)
(b) Find the open intervals on which the function is increasing or decreasing.
Increasing:
O (-∞, 0)
O (-∞, 16)
O (0, 0)
O (16, o)
Decreasing:
O (-0, 0)
O (-, 16)
O (0, o)
O (16, o)
(c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.)
relative maximum (x, y)
relative minimum (x, y)
(d) Use a graphing utility to confirm your results.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step by step

Solved in 6 steps with 26 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?
Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.
Find k so that f has a critical number at x=3
find the value of a so that the function f(x)=xeax has a critical point at x=6
Find all critical numbers in the function f(x)=7 + 3^1/3 - 2sinX on the interval 0 < x < 2π
Let f(x)=6√x−8x for x>0. Find the critical numbers
Sketch the graph of a function f that is continuous from x = 1 to x = 5 and has the given properties:a) critical numbers at 2 and 4b) from x = 1 to x = 2 decreasingc) from x =2 to x = 4 increasing d) f'' (4) = 0
What is the minimum value of f(x) = x^2 - 8 ln x on the interval [1,5]
Find the critical number of the function F(x)= x^-8In(x) X=
Find the critical numbers of the function f(x)=−6x5−15x4+10x3+2 and classify them using a graph. x = is a local max, local min or neitherx = is a x = is a
Show that 5 is a critical number of the function g(x) = 2+ (x -5)3but g does not have a local extremevalue at 5.