Derivatives and Critical Points

Welcome to the "Derivatives and Critical Points" category on Questions LLC! If you're interested in diving deep into the world of calculus and exploring the concepts of derivatives and critical points, you've come to the right place. This category serves as a hub for all your queries related to these fundamental concepts in calculus. Whether you're a student looking for assistance with homework problems or someone simply curious about these topics, our community of experts is here to help. So, go ahead and ask your questions, engage in discussions, and expand your knowledge on derivatives and critical points. Happy learning!

Questions (25)

Consider the function y = 3x5 – 25x3 + 60x + 1. Use the first or second derivative test to test the critical points. How many
1. 4 answers
2. asked by May
3. 962 views
Suppose that f(x)=x^[1/3](x+3)^[2/3](A) Find all critical values of f. If there are no critical values, enter None . If there
1. 3 answers
2. asked by Kris
3. 2,348 views
I need HELP4.The derivative of a function f is given by f'(x)=(-2x-2)e^x, and f(0) = 3. A. The function f has a critical point
1. 5 answers
2. asked by Bob
3. 455 views
Consider the function y = 3x5 – 25x3 + 60x + 1. Use the first or second derivative test to test the critical points. How many
1. 3 answers
2. asked by Olivia
3. 746 views
Consider the function h(x) = a(-2x+1)^5-b, where a doesn't equal 0 and b doesn't equal 0 are constants.A. Find h'(x) and h"(x)
1. 3 answers
2. asked by James
3. 1,503 views
Two particles move along the x-axis. For 0≤t≤6, the position of particle P is p(t)=2cos(t*π/4), while the position of
1. 4 answers
2. asked by nico
3. 2,779 views
The derivative of a function is f'(x)=x(x+2)(x-5). Find the value of x at each point where f has a(a) local maximum, (b) local
1. 3 answers
2. asked by Olivia
3. 1,128 views
Use the given derivative to find all critical points of 'f' and at each critical point determine whether a relative maximum,
1. 3 answers
2. asked by Roy
3. 1,408 views
A fundamental problem in crystallography is the determination of the packing fraction of a crystal lattice, which is the
1. 3 answers
2. asked by Sam Johnston
3. 525 views
y = (x^2 -4)/(x^2 - x -12)dy/dx of numerator I got 2x dy/dx of denomenator I got 2x - 1 dy/dx of y I got (x^2 - 16x
1. 1 answer
2. asked by Kate
3. 333 views
Determine the max & min of g(x) = x(x^2 - x^3)^3Get the derivative of the function and set it to zero, then solve for x.
1. 1 answer
2. asked by Icy
3. 359 views
Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g isg′(x)=(x^2–16)/(x−2),
1. 3 answers
2. asked by Anonymous
3. 1,493 views
The derivative of a function is f'(x)=x(x+2)(x-5). Find the value of x at each point where f has a(a) local maximum, (b) local
1. 2 answers
2. asked by Olivia
3. 966 views
How do I find the critical values?y= 4/x + tan(πx/8) What I did is I simplified it to y= 4x^-1 + tan(πx/8) then I took the
1. 3 answers
2. asked by John
3. 935 views
Find the range ofy = (3x-1)/(2x^2 + x - 6) I was going to take the derivative of the numerator and denomenator and then use the
1. 3 answers
2. asked by Kate
3. 770 views
Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2)
1. 2 answers
2. asked by Gary
3. 669 views
1. For the function f(x)=4x^3-30x^2+4:a) Find the critical numbers of f(if any); b) Find the open intervals where the function
1. 2 answers
2. asked by Rudy
3. 639 views
For y=(1/4)x^4-(2/3)x^3+(1/2)x^2-3, find the exact intervals on which the function isa. increasing b. decreasing c. concave up
1. 3 answers
2. asked by Anonymous
3. 545 views
Find the x-coordinates where f '(x) = 0 for f(x) = 2x + sin(4x) in the interval [0, π].
1. 2 answers
2. asked by Anonymous
3. 523 views
Find the x-coordinates where f '(x) = 0 for f(x) = 2x + sin(2x) in the interval [0, 2π].MY ANSWERS: x = π/2 x = 3π/2
1. 2 answers
2. asked by Someone
3. 513 views
Please check, if there is something wrong please explain what I did wrong. Thank you!Calculate the d^2y/dx^2. y= e^-x + e^x y' =
1. 2 answers
2. asked by Jade
3. 530 views
Find the critical numbers of f, find the open intervals on which the function is increasing or decreasing and use the first
1. 1 answer
2. asked by Anonymous
3. 476 views
Please help!!*f(x)= x(x+6)^1/2 find two x intercepts. Then show that f'(x)=0 at some point between the 2 x intercepts. *Use mean
1. 4 answers
2. asked by thomas
3. 463 views
Use the given derivative to find all critical points of 'f' and at each critical point determine whether a relative maximum,
1. 1 answer
2. asked by Roy
3. 452 views
a. Find the critical points of f(x)=6x^4 e^-x.b. Use the First Derivative Test to locate the local maximum and minimum values.
1. 1 answer
2. asked by mary
3. 46 views