Suppose that f : [a,b] → R is continuous and with continuous derivative f'. Suppose also that f(a) = f(b) = 0 and 1. Prove a kind of uncertainty principle, namely that cb

Q: Suppose  f ( 200 , 300 ) = 1000and ∂ f ∂ x ( 200 , 300 ) = 12 and ∂ f ∂ y ( 200 , 300 ) = 10.…

A: Given, f(200,300)=1000 ∂f∂x(200,300)=12∂f∂y(200,300)=10

Q: 34) If f is an even function that is continuous on [-1,3] and if f f(t)dt f₁f(t)dt = 8, then f…

A:

Q: 5. If ƒ1,ƒ2, ƒ3, ...‚fn are all uniformly continuous on the same domain A, then so is max (fi,f2,…

A: Given the functions f1,f2,f3,...,fn are uniformly continuous on the domain A.   A function f is said…

Q: The function f(x) = x-2 is uniformly continuous on ]2,4]. 12, 4]. True False

A:

Q: Differentiate the following function: VP - 4V U = u =||

A:

Q: A function f has f(25) = 22, f (25) = 2 and f" (x) < 0, for x ≥ 25. Which of the following are…

A:

Q: If we have that f: R → Ris a continuous function , in which f'(7) = 6 and f(7) = -2 an equation of…

A: We have to find out tangent line

Q: If f(x) is continuous at x = c then f'(c) exists. True False

A:

Q: Let F(t) = (4t³ - 1)j + (5t+2)k. Find F'(t). 7"(t) O 288t 288t³j 05+288t³ O 36t³ +5 O None of these

A:

Q: Let f(x) = ax + b/x. What are the critical points of f(x)? i

A:

Q: Let f(t) = 4t* – 4t + 5e'. Then f'(t) =

A: find the derivative

Q: (20p) Let f be a differentiable function satisfying the equation f(a + b) = f(a) + f(b) + 2ab for…

A:

Q: The speed of a car at time t, 5 ≤ 1 ≤ 10, is given by f(t)= 2(t-10)². The Mean Value Theorem…

A: The speed of a car at time  is given by  The mean value theorem gaurentees that there will be a…

Q: 1) If f(x) = x²(2), find f'(2)

A: f(x)=x2∫2xdtt2+5we know  d dx(∫axf(t)dt)=f(x)×d dx(x)-f(a)×d dx(a)

Q: 1. Find sup S and inf S (or explain why they do not exist). a) S = {xER: x² < 7x} b) S = {xER: 2x² <…

A: We have to find the supremum and infimum of the given sets

Q: Assume ƒ is a continuous on [2, 4],, and ƒ(2)= 4. Evaluate ƒ(4).

A: we have been given that f is continuous on [2,4] and f(2)=4. we have to evaluate f(4). the given…

Q: Suppose that f(x) = βx2-3     if x≤2                                   βx+2       if x &gt; 2…

A:

Q: 6. Let f be a continuous function on [0, 2] whose second derivative exists on (0, 2). Assume f(0) =…

A:

Q: ppose that f is a continuous function and the followi ƒ(2) = 2, ƒ(4) = −1, ƒ(6) = 6, ƒ(8) = = culate…

A: We have to choose the correct option from the given options according to the given information

Q: Let the function ƒ : [0, 1] →R be defined by { if x = ! (n = 1, 2, 3, · · · ) f(x) = n 1– x2…

A: Given :  f : [0, 1] →ℝ  defined by ;              fx = ex2,if  x=1n    (n=1, 2, 3, ...…

Q: Let f(x) = ²³ d. Find the value of ƒ¹ (2) af(x) 0 24 4 -8 -4 -24 12 -12 8

A:

Q: are defined c chy's mean

A:

Q: Show that Lindeberg's condition follows from Lyapounov's condition.

A: Q

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.