Derivatives and Functions

Welcome to the "Derivatives and Functions" category on Questions LLC! If you're looking to dive into the exciting world of calculus and understand the concepts of derivatives and functions better, you've come to the right place. Whether you're a calculus novice or an experienced math enthusiast, this is the perfect space for you to expand your knowledge on topics such as finding derivatives, analyzing functions, solving optimization problems, and more. Our community of experts and enthusiasts are here to help answer all your questions and guide you on your calculus journey. So, let's embark on this mathematical adventure together!

Questions (20)

Suppose that f is a differentiable function with derivative𝑓'(𝑥) = (𝑥 − 3)(𝑥 + 1)(𝑥 + 5). Determine the
1. 4 answers
2. asked by Anna
3. 1,636 views
Suppose that y = f(x) = x^2 - 4x + 4.Then on any interval where the inverse function y = f-1(x) exists, thederivative of y =
1. 4 answers
2. asked by Anonymous
3. 2,769 views
Please help! These 2 questions are very similar, and i tried to do completing square method, but i cant get the correct answer!
1. 2 answers
2. asked by Aoi
3. 611 views
Suppose the derivative of a function f is f′(x)=(x−8)^7(x−1)^4(x+19)^8.Then the function f is increasing on the interval
1. 3 answers
2. asked by Anonymous
3. 705 views
If f and g are two functions for which f' = g and g' = f for all x, then prove thatf^2 - g^2 must be a constant.
1. 4 answers
2. asked by asdasd
3. 411 views
If f'(x) = 3x^2 + 2x and f(2) = 3Then f(1) = ???
1. 3 answers
2. asked by Andrew
3. 385 views
let f'(x)=4x^3-12x^2a. find three different functions with derivative equal to f'(x) b. find the behavior
1. 2 answers
2. asked by dt
3. 595 views
A function has f''(x) = 10 and has f'(4) = 0 and f(2) = 4. Find f(x). How to approach this question?
1. 1 answer
2. asked by Leslie
3. 369 views
Suppose the derivative of a function f is f′(x)=(x−5)^3(x−3)^4(x+18)^8. Then the function f is increasing on the intervalC
1. 2 answers
2. asked by Ryan kustin
3. 501 views
Given f"(x)=-8sin3x and f'(0)=-1 and f(0)=-6. Find f(pi/5).i got stuck with f(pi/f) f"(x)=-8sin3x f'(x)=8cos3x+c
1. 3 answers
2. asked by lindsay
3. 278 views
If f(6) = 7, g(6) = 5, f '(6) = -2, and g'(6) = 8, find the following numbers.(a) (f + g)'(6) (b) (fg)'(6) How do you go about
1. 1 answer
2. asked by mike
3. 340 views
Find f.f ''(x) = 20x3 + 12x2 + 10, f(0) = 9, f(1) = 12
1. 3 answers
2. asked by Anon
3. 2,721 views
After t hours of an 8-hour trip the distance a car travels is modeled by:D(t)= 10t + (5)/(1+t) - 5 where D(t) is measured in
1. 1 answer
2. asked by Aletha
3. 994 views
Og Function: -cos(3x)Derivative Function: 3 sin(3x) The period for the function and its derivative is 2π/3 radians. Over one
1. 2 answers
2. asked by Anonymous
3. 935 views
(a) find the intervals on which f is incrs or decrs.(b) find the local min/max values of f. (c) find the intervals of concavity
1. 3 answers
2. asked by Riley
3. 720 views
The position function of a particle is given by s(t) = t^{3}-3t^{2}-7t, t\ge 0 where s is measured in meters and t in seconds.Wh
1. 2 answers
2. asked by STEPH
3. 612 views
find the intervals where the function is increasing and the intervals where it is decreasingf(x)= (x^3/3)-(x^2/2) ok i found its
1. 2 answers
2. asked by Katia
3. 623 views
Given f(x)=sin(x)-2cos(x) on the interval [0,2pi].a) Determine where the function is increasing and decreasing. b) Determine
1. 2 answers
2. asked by Shawn
3. 620 views
Let f(x)= x^5-5x+31-Find f'(x) and f"(x). 2-Find the intervals on which f(x) is increasing or decreasing. 3-Find the local
1. 1 answer
2. asked by Haneen
3. 482 views
h(x)= x + cos(ax), where a is a positive constant such that 0 < a < 4.What values of a make h(x) strictly decreasing? I know
1. 1 answer
2. asked by kaitlyn
3. 470 views