Derivatives and Optimization

Welcome to the "Derivatives and Optimization" category on Questions LLC! If you are interested in exploring the fascinating world of calculus, numerical analysis, and problem-solving techniques, you've come to the right place. This category is dedicated to answering questions related to derivatives – the mathematical tool used to understand the rate of change of a function at any given point – and optimization – the process of finding the maximum or minimum value of a function. Whether you're a student looking for help with homework, a math enthusiast seeking to deepen your understanding, or a professional looking for practical applications, our community is here to provide insightful answers and guidance. So dive in, ask your questions, and let's embark on this journey of derivatives and optimization together!

Questions (16)

The graph of f ′(x), the derivative of x, is continuous for all x and consists of five line segments as shown below. Given f
1. 5 answers
2. asked by Alice
3. 7,699 views
The average cost of manufacturing a quantity q of a good, is defined to bea(q) = C(q)/q. The average cost per item to produce q
1. 4 answers
2. asked by Jasmine
3. 6,631 views
R=M^2(c/2-m/3)dR/dM=CM-M^2 I found the derivative. Now how would I find the vale of M that maximize the derivative dR/dM? set it
1. 3 answers
2. asked by Anonymous
3. 2,505 views
The distance meters from a fixed point O, covered by a particle after t seconds given by the equation; S = t3 – 6t2 + 9t + 5.(
1. 3 answers
2. asked by kudu
3. 523 views
The function f(x) is defined as f(x) = -2(x+2)(x-1)^2 = -2(x^3 -3x + 2) on the open interval (-3,3). 1. Determine the
1. 3 answers
2. asked by Madeline
3. 517 views
The graph of f ′(x), the derivative of x, is continuous for all x and consists of five line segments as shown below. Given f
1. 4 answers
2. asked by ah
3. 3,509 views
If f(x) = ln(x^2 + 9)a) find the local maximum and minimum values I found the derivative and set it equal to 0 but idk what to
1. 1 answer
2. asked by Loon
3. 381 views
1) find x' then find x''(t)=-10 . x'=- and x(1)=6how do you start? find absolute max and min of f(x) = x/lnx from [sqrt e, e^4)
1. 1 answer
2. asked by Anonymous
3. 194 views
1. Find all points of inflection of the function f(x)=x^4-6x^3A. (0, 0) B. (0, 0), (9/2, -2187/16) C. (3, -81) D. (0, 0), 3,
1. 2 answers
2. asked by Anonymous
3. 793 views
Let U(x; y) = 5x:8y:2 showing all derivation work, find:(a) the Marshallian demand functions for x and y (b) the Indirect
1. 2 answers
2. asked by Anonymous
3. 519 views
the relationship between the dosage, x, of a drug and the resulting change in body temperature is given by f(x)=x squared(4-x)
1. 1 answer
2. asked by Olivia
3. 346 views
Profit=p(-p^2+33p+9)-9(-p^2+33p+9)+100How do I simplify this so I can take the derivative For Further Reading * Calc - Michael,
1. 11 answers
2. asked by Ben
3. 1,076 views
Given demand curve P=400-.05Q, at what price is total revenue maximized?There are a number of ways to do this problem. Let me
1. 1 answer
2. asked by greg
3. 450 views
h(x)= x + cos(ax), where a is a positive constant such that 0 < a < 4. For what values of a will h(x) have a relative maximum at
1. 4 answers
2. asked by ashley
3. 737 views
Let f(x) be a twice differentiable function (i.e. f(x), f′(x) and f′′(x) are defined for all x), and let a ∈ R (a is a
1. 1 answer
2. asked by Kenny
3. 634 views
Hi i need help in this. Some of the parts i got the answer but some i don't. please help!A ship uses $(7v^2) of fuel per hour
1. 1 answer
2. asked by Becky
3. 435 views