Mvt Definition and 26 Threads

The tutorial question I am working on is, (a) Attempt We can use mean value theorem since ##(c: \mathbb{R} \rightarrow \mathbb{R}~countinity ) \implies (c: [-d, d] \rightarrow [c(-d), c(d)]~countinity)## Thus ##c: [-d, d] \rightarrow [c(-d), c(d)] ## is differentiable on ##(-d, d)##, then...

$10 min = \dfrac{h}{6}$ So $a(t)=v'(t) =\dfrac{\dfrac{(50-30)mi}{h}}{\dfrac{h}{6}} =\dfrac{20 mi}{h}\cdot\dfrac{6}{h}=\dfrac{120 mi}{h^2}$ Hopefully 🕶

Ok Just have trouble getting this without a function..

$\tiny{3.2.15}$ Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. Graph the function the secant line through the endpoints, and the tangent line at $(c,f(c))$. $f(x)=\sqrt{x} \quad [0,4]$ Are the secant line and the tangent line parallel...

Hi there I'm prepping for a big test tomorrow and I'm really struggling with this question:If f′′(x)≥−1, x belongs to (−15,15), and f′(1)=3, find the interval over which x is definitely increasing.I'm struggling with substitution because I just don't seem to have enough values. Is there a...

Homework Statement http://prntscr.com/daze68 What I don't understand: 1. "P be a polynomial with degree n" do these equations satisfy this description?: $$p(x) = (x^2 + x)^n$$ $$p(x) = (5x^2 + 2x)^n$$ etc. 2. "C1 is a curve defined by y=p(x)" c1 is essentially just the curve of the...

Homework Statement Show that The tangent at (c,ec) on the curve y=ex intersects the chord joining the points (c-1,ec-1) and (c+1,ec+1) at the left of x=c Homework Equations Legrange's mean value theorem The Attempt at a Solution f'(c)=ec Applying LMVT at c-1, c+1...

Homework Statement for ##0<\alpha,\beta<2##, prove that ##\int_0^4f(t)dt=2[\alpha f(\alpha)+\beta f(\beta)]## Homework Equations Mean value theorem: ##f'(c)=\frac{f(b)-f(a)}{b-a}## The Attempt at a Solution I got the answer for the question but I have made an assumption but I don't know if...

Homework Statement Let ###f## be double differentiable function such that ##|f''(x)|\le 1## for all ##x\in [0,1]##. If f(0)=f(1), then, A)##|f(x)|>1## B)##|f(x)|<1## C)##|f'(x)|>1## D)##|f'(x)|<1## Homework Equations MVT: $$f'(c)=\frac{f(b)-f(a)}{b-a}$$ The Attempt at a Solution I first tried...

Can anyone give me an easy way to find extremas and how to use the mean value theorem. This is the first thing in calculus where I read and reread and have no idea what to do when I get to the problems. It just doesn't make sense to me.. Any help is appreciated. Thank you. EDIT: Basically my...

1. Homework Statement Give a graphical argument that if f(a)=g(a) and f'(x)>g'(x) for all x>a, then f(x)>g(x) for all x>a. Use the Mean Value Theorem to prove it. 2. Homework Equations 3. The Attempt at a Solution I have sketched a graphical argument to show that f(x)>g(x)...

1. Homework Statement Give a graphical argument that if f(a)=g(a) and f'(x)>g'(x) for all x>a, then f(x)>g(x) for all x>a. Use the Mean Value Theorem to prove it. 2. Homework Equations 3. The Attempt at a Solution I have sketched a graphical argument to show that f(x)>g(x)...

I'm so bad with the Mean Value Theorem. Can someone help me prove that, if f(x)=sinx, that, for any given a and b, |sinb-sina|<=|b-a|. Explain if you could too, please. Thanks a lot.

Excuse the typing please, as I am posting from my phone. Let f have domain [0,infty) and range in R. Suppose as x goes to infinity, f'(x) goes to a constant b. I wish to show that f(x)/x goes to b as x goes to infinity. I have tried numerous applications of the MVT to solve this and cannot...

Homework Statement Consider the function g: [0,∞) -> R defined by G(x)=x+e-2x A. Use the mean value theorem to prove that |g(x2)-g(x1)|<|x2-x1| for all x1,x2 E [0,∞) with x1≠x2. B. Find all fixed points of g on [0,∞). Homework Equations MVT: f'(c) = f(b)-f(a)/b-a. The Attempt...

Hello! The Mean Value thereom gives F(b)-F(a) = f(c).(b-a) Where f is F' and c is the value of x at which it's derivate is equal to the average rate of change over the interval a to b for F. The Fundamental thereom of calculus also gives F(b)-F(a) = (\frac{1}{b-a} \left \left \int...

Homework Statement Prove for all real x and y that |sinx - siny| <= |x-y| Homework Equations It's a question from the Mean Value Theorem/Rolle's Theorem section. The Attempt at a Solution Honestly, I've tried. It looks somewhat similar to the triangle inequality (I think?), but...

Homework Statement The mass, m(t), in grams, of a tumor t weeks after it begins growing is given by m(t) = [te^t] / 80 . What is the average rate of change, in grams per week, during the fifth week of growth? a.) 2.730 b.) 3.412 c.) 6.189 d.) 6.546 e.) 11.131 Homework...

suppose f and g are continues on [0,1] and differentiable on (0,1) and f'(x)g(x) differs f(x)g'(x) for every x existing in (0,1) prove that there is a point c in [0,1] so g(c)=0 ?? for what purpose do i need to know that "f and g are continues on [0,1] and differentiable on (0,1)...

suppose f is a continues function on point x_0 prove that g(x)=(x-x_0)*f(x) differentiable on x_0?? calculate g'(x_0) i tried to think like this: if f(x) is continues on x_0 then lim f(x) as x->x_0 equals f(x_0) mvt says f'(c)=[f(a)-f(b)] cauchys mvt says...

Homework Statement -x<sin(x)<x Homework Equations show the inequality using the mean value theorem. The Attempt at a Solution i try to find c but i keep getting tan(x) as the solution.

Homework Statement Give an example of a function (necessarily discontinuous) that does not satisfy the conclusion of MVT for Integrals Homework Equations MVT for \int = \frac{1}{b-a}\int ^{b}_{a} f(x) dx The Attempt at a Solution So I should need one point of discontinuity on every interval...

Homework Statement Let f be diff. on (0,infinity) If the limit of f'(x) as x->infinity and limit of f(n) as n->infinity both exist and are finite, prove limit of f'(x) as x->infinity is 0. Homework Equations Mean Value Theorem (applied below) The Attempt at a Solution Suppose a>0 and b>0...

The following two questions are practice problems that I have been stuck on. Homework Statement Use the Mean Value Theorem to show that e^x > 1 + x for all x > 0 Homework Equations Mean Value Theorem: If f: [a,b] to R is continuous on [a,b] and differentiable on (a,b) then there...

Homework Statement I am trying to see the geometric interpretation of the generalized MVT. It is not a homework problem, but would like to know how to interpret the equation Homework Equations [f(b)- f(a)]* g'(x) = [g(b)- g(a)]* f'(x) The Attempt at a Solution On...

Hello everyone, I'm stuck on a MVT question. Can someone please help me out? Its not really a homework question, I'm doing this question to enhance my understanding of various things. Q. Where a < x_0 < b, suppose that f(x) is differentiable in (a,b) and f'(x_0) = 0. Suppose also that for...