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: Suppose f: (a, b) →→ R is differentiable. True or false: If f is unbounded, then f' (the derivative…

A: f:a, b→ℝ is differentiable.

Q: 3. Let f be continuous on [-1, 4] and differentiable on (-1,4). If f(-1) = –1 and f(4) = 4, then the…

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…

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

A:

Q: Find the derivative of y = = Ve-5t +1 dy dt ||

A:

Q: sume that f(t) is continuous on [a, b| and that u = g(t) is cont ferentiable on [a, b], then f(u)…

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Use the second-derivative test to show that the function f(x, y) = x²eY – y²e* has a saddle point at…

A: A point (a,b) of function f(x,y) is said to be the saddle point if it is a critical point…

Q: of af and Let f(x, y, A) = xy + A(5 – x – y). Find· ax' əy` af

A: f(x,y,λ)=xy+5λ-λx-λy .....(1) Differentiating (1) partially with respect to x, ∂f∂x=(1)y+0-λ-0…

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

A:

Q: f(x) = log,(\a² x ·7*) log, (ya²x •7*).

A:

Q: Suppose that f'(x) > M for all x E [a, b]. Prove that f(b) > f(a) + M(b

A: Since  f'(x)≥M therefore the function is differentiable and hence continuous let f is continuous on…

Q: Exercise 4: Suppose f is differentiable on (2,6) and continuous on [2,6. Suppose further that 1 < f'…

A: Given:f is differentiable on (2, 6) and continuous on [2, 6].

Q: Suppose f, g:C → C are differentiable. Prove that fg is differentiable and that (fg)' = f'g + fg'.

A:

Q: Determine whether the statement is true or false. '8 If f'is continuous on [7, 8], then f '(v) dv =…

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Q: Prove that if f'(z)=0 then f(z) is a constant.

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Q: Let h(x) = f(g(x)). If: f(3) = 0, f'(42) = –5, f'(3) = 4, g(3) = 42, & gʻ (3) = 0, then h'(3) =

A:

Q: find the local max and min values and saddle points of the function f(x,y)=xy*(1-x-y)

A: Consider the function f(x, y) = xy(1 – x – y).To find the local maximum and minimum values and…

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: Let f(x) = e*. What is f' (3)?

A: Differentiate wrt x

Q: If f has a derivative at x = 2, then f is continuous at x = = 2. True False

A:

Q: r9(z) f(t) dt without using the Fundamental Theorem of 6. Find the derivative of y = Calculus part…

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

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

A:

Q: If fCxl is continuous on [2,7],then Si f(u) dvz f (7)-(2) True e or false?

A: we have given that f(x) is continuous on[2,7].

Q: are defined c chy's mean

A:

Q: Fermat’s Theorem does not claim that if f'(c) = 0, then f (c) is a local extreme value (this is…

A: The given statement is “Fermat’s Theorem does not claim that if f'(c) = 0, then f (c) is a local…

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.