5 5. Curve sketching: Sketch the graph of a continuous function f satsifying all of the following properties:(a) f(-2) = 2, f(3) = -2(b) f'(x) < 0 on (-00, -4) and (0, 3), and f'(x) > 0 on (-4, 0) and (3, o0)(c) f"(1) > 0 on (-00, -2) and (5, 00) and f" < 0 on (-2,5)Note: your answer must consist of just ONE graph!

Given properties: f-2=2, f3=-2 f'x<0 on -∞,-4∪0,3f'x>0 on -4,0∪3,∞ f''x>0 on…

Answered: Curve sketching: Sketch the graph of a…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 1E

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Sketch the graph of a differentiable function y = ƒ(x) through the point (1, 1) if ƒ′(1) = 0 and a. ƒ′(x) > 0 for x < 1 and ƒ′(x) < 0 for x > 1; b. ƒ′(x) < 0 for x < 1 and ƒ′(x) > 0 for x > 1; c. ƒ′(x) >0 for x ≠ 1; d. ƒ′(x) < 0 for x ≠ 1.
1). Sketch a continuous function f on the interval [-6, 6] that has the following properties: x-intercepts: (-3, 0) and (2, 0) critical values: f ’(x)=0 for x-values -5, -2, 0, 4 f ’(x)>0 on: (-5, -2), (-2, 0), (4, 6] f ’(x)<0 on: [-6, -5), (0,4) f ‘’(x)>0 on: [-6, -3), (-2, -1), (2, 6] f ‘’(x)<0 on: (-3,-2), (-1,2) Provide all work please. 2.) Use linear approximation to estimate the following quantity. Choose avalue of “a” to produce a small error. Make sure to write out the appropriate L(x) before finding L(82). Leave exact answer (in fraction form) √82
1). Sketch a continuous function f on the interval [-6, 6] that has the following properties: x-intercepts: (-3, 0) and (2, 0) critical values: f ’(x)=0 for x-values -5, -2, 0, 4 f ’(x)>0 on: (-5, -2), (-2, 0), (4, 6] f ’(x)<0 on: [-6, -5), (0,4) f ‘’(x)>0 on: [-6, -3), (-2, -1), (2, 6] f ‘’(x)<0 on: (-3,-2), (-1,2) Provide all work please.
consider a continuous function y = f(x) whose first derivative is y = x(x – 2). The function f has a local/relative minimum value when x = choices: a. 2 b. 1 c. 0 d. -2
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Curve sketching: Sketch the graph of a contimuous function f satsifying all of the following properties: (a) f(-2) = 2, f(3) = -2 (b) f'(x) < 0 on (-0, -4) and (0, 3), and f'(x) > 0 on (-4, 0) and (3, o0) (c) f"(r) > 0 on (-0, -2) and (5, o0) and f" < 0 on (-2,5)