Question

what is the difference between mean value theorem and Rolls theorem?? ❤❤​

Answer 1

$\huge\boxed{\underline{\mathcal{\red{W} \green{hi} \pink{z} \orange{Kid} \blue{A} \pink{man}}}}$

➲ ʏᴏᴜʀ ǫᴜᴇsᴛɪᴏɴ:⍰

what is the difference between mean value theorem and Rolls theorem??

━━━━━━━༺۵༻━━━━━━━

➻❥ᴀɴsᴡᴇʀ:☑$<font color="Orange">$

Mean Value Theorem

f '(c) = (f(b) - f(a)) / (b - a). (The Mean Value Theorem claims the existence of a point at which the tangent is parallel to the secant joining (a, f(a)) and (b, f(b)). Rolle's theorem is clearly a particular case of the MVT in which f satisfies an additional condition, f(a) = f(b).)

━━━━━━━༺۵༻━━━━━━━

$<marquee><font color="Red"><h1>⛄Thoko Like✌️Mark me As Brainliest✌️</marquee>$

Answer 2

Answer:

Mean value theorem. The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b].

Step-by-step explanation:

Mean Value Theorem (MVT):

If is continuous on the closed interval and differentiable on the open interval , then there is a number in such that

or, equivalently,

In words: there is at least one value between and where the tangent line is parallel to the secant line that connects the interval’s endpoints. (See the figures.)

When the Mean Value Theorem applies, the slope of the tangent line at x=c is the same as the slope of the secant line connecting the endpoints of the interval.

[Click on a figure to see a larger version.]

Rolle’s Theorem:

In Calculus texts and lecture, Rolle’s theorem is given first since it’s used as part of the proof for the Mean Value Theorem (MVT). You can easily remember it, though, as just a special case of the MVT: it has the same requirements about continuity on and differentiability on , and the additional requirement that . In that case, the MVT says that

Since (or there’s no interval), we know

Hence when we must have

In words: when the slope of the secant line connecting the endpoints is zero, and hence there is at least one value between and where the tangent line has zero slope. (See the figures.)

When Rolle's theorem applies, there is a point c in the interval where the tangent line to the function has zero slope.

The problems below illustrate some typical uses of the Mean Value Theorem and Rolle’s Theorem.