L23 - L23 – Mean Value Theorem Rolle’s Theorem – Let...

Info iconThis preview shows pages 1–14. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: L23 – Mean Value Theorem Rolle’s Theorem – Let f be a function that satisfies the following properties: 1. 2. 3. The there is a c in ( a, b ) such that 1 Graphically 2 Show that f (x) = x3 + 3x − 2 has exactly one real root. 3 Find the value of c implied by Rolle’s Theorem for f (x) = (2x − x2 ) 3 on [ 0, 2 ] . 2 4 Find the value of c implied by Rolle’s Theorem for g (x) = cos(πx) on [ 0, 2 ] . 5 Mean Value Theorem – Let f be a function that satisfies 1. 2. Then there is a c in ( a, b ) such that 6 Equation of the secant line to f passing through ( a, f (a) ) and ( b, f (b) ) has slope: Equation – Consider h(x) = f (x) − y h(x) is 1. 2. 7 h(a) = h(b) = By Rolle’s Theorem – 8 Find the value of c implied by the Mean Value Theorem for f (x) = x3 − x2 − 2x on [ −1, 1 ] . 9 The position of an object dropped from 650 ft is s(t) = 650 − 16t2 , where t is in seconds. Find the average velocity on [ 0, 5 ] seconds. Use the Mean Value Theorem to verify that at some time in the first five seconds, average velocity = instantaneous velocity. 10 If f (x) = on [ 0, 3 ] . 13 x + 2x find the value of c guaranteed by the Mean Value Theorem 3 11 Use the Mean Value Theorem to show that | cos(x) − cos(y ) | ≤ | x − y | . 12 Suppose f (0) = 4 and f (x) ≥ −2 for all values of x, how small can f (3) be? 13 Theorem – If f (x) = 0 for all x in an interval ( a, b ), then Corollary – If f (x) = g (x) for all x in an interval ( a, b ), then f − g is i.e. f (x) = 14 ...
View Full Document

Page1 / 14

L23 - L23 – Mean Value Theorem Rolle’s Theorem – Let...

This preview shows document pages 1 - 14. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online