Use the mean value theorem and sketch a graph to interpret geometrically. See image Mean Value Theorem:F(b) - F (a)F'le)=b-aApply to the function F(x)=x3-3xon the indicated interval I to find allnumbers, c,in the nterior of I, whichsatısfy the conclusion of this theromSketch' the araph of the functionon° the interval I. Interpretgoometrically- tangent and secant lines.(3-3X%3Dy=F(x)a) I t {-1, +2}

Answered: Image /qna-images/answer/5c9a8300-4216-4eef-8eb2-31ab0a87d0f1.jpg

Mean Value Theor em: F(b) - F (a) b-a Apply to the function F(x) = x ³ - 3X on the indicated interval I to find all numbers,c, in the interior of I, which satısfy the conclusion of this therom. Sketch' the qraph of the function y=F(x) goometrically- on the interval I. Interpret tangent and Secant lines. | a) I = {-1, +2}

Mean Value Theor em: F(b) - F (a) b-a Apply to the function F(x) = x ³ - 3X on the indicated interval I to find all numbers,c, in the interior of I, which satısfy the conclusion of this therom. Sketch' the qraph of the function y=F(x) goometrically- on the interval I. Interpret tangent and Secant lines. | a) I = {-1, +2}

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 78E

See similar textbooks

Similar questions

The Second Derivative Test Use the Second Derivative Test to locatethe local extrema of the following functions.a. f(x) = 3x 4 - 4x 3 - 6x 2 + 12x + 1 on [-2, 2] b. f(x) = sin2 x
A right triangle has one vertex on the graph of y = x3, x > 0, at (x, y) another at the origin, and the third on the positive y-axis at (0, y). Express the area A of the triangle as a function of x.
f(x,y)=(x+y) sin 1/(x-1) sin 1/(y+1) the limit of the function is 0 at the point (1, -1), the limit .Prove it using the definition.
Consider the function on the interval (0, 2π). f(x) = sin x + cos x (a) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) increasing decreasing (b) Apply the First Derivative Test to identify the relative extrema. relative maximum (x, y) = relative minimum (x, y) =
Mean Value Theorem: If f is a continuous function on the closed interval [a,b] & differable on the open interval (a,b), then there exists such numbers, c, on that f’(c)=[f(b)-f(a)]/b-a. Sketch the graph of a function that satisfies both the hypothesis and conclusion of the mean value theorem. Mark on the graph the value(s) of c and the corresponding tangent line to the curve guaranteed by the MVT
f ''(x) = x2(x − 5)4(x + 6)3(x2 − 1). Suppose f has horizontal tangent lines at the following x-values: x = −7, 1/2, 0, 6, −2. Determine the x-values that correspond to a local maximum, a local minimum, or that cannot be determined by the second derivative test. (Enter your answers as a comma-separated list.)
Find the absolute extremas as well as all values of x where they occurson the specified domain. 4)f(x) =1/3x^3 - 2x^2 + 3x - 4; [-2, 5] Determine all values on the interval that hold for the mean value theorem 5) f(x) = x^3 + 12x + 36 on [-2,5] 1) A small frictionless cart, attached to the wall by a spring, is pulled 10 cm back from its rest position and releasedat time t = 0 to roll back and forth for 4 sec. Its position at time t iss = 1 - 10 cos pi t. What is the cart's maximum speed? When is the cart moving that fast? What is the magnitudeof of the acceleration then?
Consider the function on the interval (0, 2?). f(x) = x − 2 sin x (a)Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) increasing decreasing (b)Apply the First Derivative Test to identify the relative extrema. relative maximum (x, y) = relative minimum (x, y) =
The tangent line to the graph of f(x) at x = 2 is shown. On the tangent line, P is the point of tangency and A is another point on the line. The x y-coordinate plane is given. There is 1 curve and 1 line on the graph. The curve enters the window in the second quadrant, goes down and right becoming less steep, passes through the point (−1, 2.5) crossing the line, crosses the y-axis at approximately y = 1.3, becomes nearly horizontal at the approximate point (1, 1.2), goes down and right becoming more steep, passes through the point (2, 1) touching the line, crosses the x-axis at approximately x = 2.9, and exits the window in the fourth quadrant. The line enters the window in the second quadrant, goes down and right, passes through the point (−1, 2.5) crossing the curve, crosses the y-axis at y = 2, passes through the point (2, 1) touching the curve, crosses the x-axis at x = 4, and exits the window in the fourth quadrant. Point P occurs at (2, 1). Point A occurs at (−2, 3). (a)…
A particle moves along a line. Its position x (incentimeters to the right of the origin) is a function of time t(in seconds) shown by the graph to the right.(a) identify value(s) of t which are critical numbersfor the position function x(t)(b) identify values of t which correspond to inflectionpoints on the graph of x(t)t x (c) identify a t-interval on which x(t) increases and the graph of x(t) is concave down. (d) identify a t-interval on which the velocity x0(t) is negative and the acceleration x00(t) is positive.(e) identify a t-interval on which both the position x(t) and the velocity x(t) are decreasing. Plese solve that with detailed solution.
Consider the function on the interval (0, 2π). f(x) = 9 sin2(x) + 9 sin(x) (a) Find the open interval(s) on which the function is increasing or decreasing. (Enter your answers using interval notation.) (b) Apply the First Derivative Test to identify all relative extrema. relative maxima (x, y) = (smaller x-value) (x, y) = (larger x-value) relative minima (x, y) = (smaller x-value) (x, y) = (larger x-value)
For the function f(x)=x +2cos x on the interval [0,2?]:a) Find the critical values.b) Find the open intervals on which f is increasing or decreasing using sign analysis.c) Find the relative extrema using the first derivative test.d) Find the relative extrema using the second derivative test.e) Find the intervals of concavity.f) Find any inflection points (?, ?).2. Sketch the graph of a function with the following characteristics:a) ?(2) = ?(4) = 0b) ?(?) > 0 ??? ? < 3c) ?(3) ???? ??? ?????d) ?(?) < 0 ??? ? > 3e) ?"(?) > 0, ? ≠ 3