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Suppose that a curve C in the
(a) Let m and M denote the respective minimum and maximum values of
(b) Use part (a) to prove that max
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EBK CALCULUS EARLY TRANSCENDENTALS SING
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Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus and Its Applications (11th Edition)
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Glencoe Math Accelerated, Student Edition
- 1. A function of two variables is given f(x, y) = x² + y² + e-(x²+y²) a) Draw a picture of the graph of the function f. Use for example Geogebra. b) Find a tangent plane to the graph of the function f at all points (x, y, f(x, y)) c) At what points is the tangent plane parallel to the xy-plane? How does the function behave near the points (0, 0)?arrow_forwardCompute F · dr where F(x, y) = <2x+1,y> and C is the path traced by the line segment starting at (0, −1) and ending at (1, 0), followed by the half circle of radius one above the x-axis runningcounterclockwise from (1, 0) to (−1, 0).arrow_forwarda) Find the directional derivative of the function f(x, y, z) = x² y? (2z+1)² at the point P:(1, – 1, 1) and in the direction of a =[3, 3, 0]. b) Find the direction of maximum decrease of f at the point P. Maximum file size: 100MB. maximum number of files: 1arrow_forward
- o'pg. 156-159 J #1.) Determine f' and F", if (x)=x²-14 X4 #2.) For y = x9-7x³ +2, find d²y dx2 #6) Determine the maximum and a f(x) = 2x³-9x², -2≤ x ≤ 4 minimum of each function on the given interval b) f(x) = 12x - x³, x= [-3,5] (²) f(x) = 2x + 18,1 fcx)=x²-2x + 6₁-1 ≤ x ≤7 b) f(x)= x³ + x², -3 ≤ x ≤ 3 Cf(x)= x³-12x + 2,-5 ≤ x ≤ 5 d.) f(x) = 3x5-5x³, -2≤x≤4arrow_forwardFind the maximum value of of Iƒ" (x) [0,2] f(x)=√1+x² HINT: Much like the previous question except that you are focussing only on the max. Input your function as surd((1+x^2),2); Let your second derivative function equal abs(df2); assuming that df2 is the second derivative. Substitute your endpoints 0 and 2 into your absolute value second derivative function. Find third derivative and solve it for x. Substitute the result obtain into your second derivative absolute value function. Compare all y-values obtained for maximum value. 5) on the indicated interval. 6) Without the aid of a graph, find the absolute maximum and minimum values of the functionarrow_forward6. (a) Let I be an interval and ~r₁(t) = (x₁(t),y₁(t),z₁(t)) where t€ 1, be two differentiable curves in R³ Show that i. ii. and ~r₂(t) = (x₂(t),y₂(t),z2(t)), d (F₁(t) · F₂(t)) = ri(t) · F₂(t) + Fi(t) · F₂(t) dt d dt (b) * Suppose that I is an interval and (Fi(t) × F₂(t)) = T₁(t) × ²₂2(t) + r₁(t) × F2(t) X ~r(t) = (x(t),y(t),z(t)), where t € I, is a twice-differentiable curve that describes the position of an object in R³. If the object is moving at a constant speed, show that its velocity is always perpendicular to its acceleration.arrow_forward
- Asaparrow_forwardFind relative maximum and or minimumarrow_forwardSuppose that z is an implicit function of x and y in a neighborhood of the point P = (0, −3, 1) of the surface S of equation: exz + yz + 2 = 0 An equation for the tangent line to the surface S at the point P, in the direction of the vector w = (3, −2), corresponds to:arrow_forward
- These two questions are from multivariable calculus.arrow_forward4. Let f (x) = x³ -x² + 5. a) Find the y-intercept of f. y-intercept: b) Find f' and f", and determine where each are 0 and/or do not exist (DNE). If none, write "none". f' = 0: f' DNE: f" = 0: f" DNE: c) E Do a sign analysis on f' and f". d) Find the intervals on which f is increasing and decreasing. Increasing: Decreasing: e) Find the intervals on which f is concave up and concave down. Concave up: Concave down: f) answers as (x, y) points. Find all local maxima, local minima, and inflection points of f. Be sure to write your Local max: Local min: Inflection point(s): -4 -3 -1 g) Sketch the graph of f.arrow_forwardNo. 6 (a, b, c)arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
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