Given: f(x) = x3+ x2+4x find the following:
Given: f(x) = x3+ x2+4x find the following:
a) Relative extrema b) Table of values c) x-intercepts (if any) d) y-intercept e) Domain f Range g) Interval(s) increasing h) Interval(s) decreasing i) Find All zero s ) Factor completely k) Graph
Homework Answers
For g(x) = 3x2-12x + 6, answer the following questions.
For g(x) = 3x2-12x + 6, answer the following questions. a. Find the values of the x-intercepts b. State the coordinates of the y-intercept. c. State the vertex d. State the axis of symmetry e. State the direction of the parabola. f. Decide whether there is a relative maximum or minimum, then state it. g. Graph the function accurately using the above information. h. State the domain. i. State the range. j. State the interval of x where the graph is increasing k. State the interval of x where the graph...
A quadratic function f is given. flx) = -x2. 4x 3 (a) Express f in transformation...
A quadratic function f is given. flx) = -x2. 4x 3 (a) Express f in transformation form. f(x) (b) Find the vertex and x and y-intercepts of f. (If an answer does not exist, enter DNE.) (x, y) vertex (x, y) (smaller x-value) x-intercepts (x, y) (larger x-value) (x, y) yintercept (c) Sketch a graph of f. Tools Actions Clear Al 1. Select an object from the Tools menu to the left. Delato 2. Enter coordinates in Object Properties below,...
16 For the quadratic function f(x) = -x2 - 8x, answer parts (a) through (c) (a)...
16 For the quadratic function f(x) = -x2 - 8x, answer parts (a) through (c) (a) Graph the quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and X-intercepts, if any. Does the graph off open up or down? 12 8- up Odown 2015 12 118 12 16 What are the coordinates of the vertex? The vertex of the parabola is (Type an ordered pair. Use integers or fractions...
5. Find where the function f(x) = 2x4 - 4x?- 5 is increasing and decreasing, and...
5. Find where the function f(x) = 2x4 - 4x?- 5 is increasing and decreasing, and find the relative extrema. 6 6. Find the absolute extrema of the function f(x) + over the interval (1,6]. I
Name: 1. For the function f(x) = x2 – 1 find and simplify: a. f(-2) b....
Name: 1. For the function f(x) = x2 – 1 find and simplify: a. f(-2) b. f(-x) c. -f(x) d. f(x - 2) 2. Find the domain of each function below. Write your answer in interval notation. a. f(x) = x + 2 x2 + x - 6 b. 8(x) = (2x - 1 1 f(x + h) - f(x) 3. For the function f(x) = 2x2 – 3, find the difference quotient h 4. Use the graph of the...
11. As a general overview, these are the details one needs to look for when sketching...
11. As a general overview, these are the details one needs to look for when sketching curves (in no particular order: a Domain and range f. Relative extrema (maximum and minimum b. x-and y-intercepts values) c. Vertical asymptotes 9. Absolute extrema (maximum and minimum d. End behavior (including horizontal or values) polynomial asymptotes) h. Intervals of concavity e Intervals of increasing and decreasing i. Points of inflection behavior j. Other points of interest (corners, cusps, vertical tangents, discontinuities, etc) x3-3x...
find an equation of the tangent plane and parametric equations of the normal line to the surface at the given point z=-9+4x-6y-x^2-y^2 (2,-3,4) Find the relative extrema. A) f(x, y) = x3-3xyザ B)...
find an equation of the tangent plane and parametric equations
of the normal line to the surface at the given point
z=-9+4x-6y-x^2-y^2 (2,-3,4)
Find the relative extrema. A) f(x, y) = x3-3xyザ B) f(x, y)=xy +-+-
Find the relative extrema. A) f(x, y) = x3-3xyザ B) f(x, y)=xy +-+-
The function f is defined as follows. f(x)- 4x-3 if x21 (a) Find the domain of the function. (b) Locate any intercepts....
The function f is defined as follows. f(x)- 4x-3 if x21 (a) Find the domain of the function. (b) Locate any intercepts. (c) Graph the function. (d) Based on the graph, find the range. (e) Is f continuous on its domain?
The function f is defined as follows. f(x)- 4x-3 if x21 (a) Find the domain of the function. (b) Locate any intercepts. (c) Graph the function. (d) Based on the graph, find the range. (e) Is f continuous on...
A Guide to Curve Sketching 1. Determine the domain of f. 2. Find the x- and...
A Guide to Curve Sketching 1. Determine the domain of f. 2. Find the x- and y-intercepts off.* 3. Determine the behavior of f for large absolute values of x. 4. Find all horizontal and vertical asymptotes of the graph of f. 5. Determine the intervals where f is increasing and where f is decreasing, 6. Find the relative extrema of f. 7. Determine the concavity of the graph of f. 8. Find the inflection points of f. 9. Plot...
1. Consider the curve given by the function f(x) = -4.83 27(x + 1)2 You are...
1. Consider the curve given by the function f(x) = -4.83 27(x + 1)2 You are given that -4x²(x +3) - 8.1 f'(x) = and f"(x) = 27(x + 1)3 9(x + 1)4 Compile the following information about f(x) and its graph. Show your work to justify your answers to parts (f), (g), (h), (i) and (j). Otherwise, give answers only. Answer "NONE” if the function does not display a feature listed. 1] (a) Domain of f (b) x and...
A quadratic function f is given. flx) = -x2. 4x 3 (a) Express f in transformation form. f(x) (b) Find the vertex and x and y-intercepts of f. (If an answer does not exist, enter DNE.) (x, y) vertex (x, y) (smaller x-value) x-intercepts (x, y) (larger x-value) (x, y) yintercept (c) Sketch a graph of f. Tools Actions Clear Al 1. Select an object from the Tools menu to the left. Delato 2. Enter coordinates in Object Properties below,...
16 For the quadratic function f(x) = -x2 - 8x, answer parts (a) through (c) (a) Graph the quadratic function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and X-intercepts, if any. Does the graph off open up or down? 12 8- up Odown 2015 12 118 12 16 What are the coordinates of the vertex? The vertex of the parabola is (Type an ordered pair. Use integers or fractions...
5. Find where the function f(x) = 2x4 - 4x?- 5 is increasing and decreasing, and find the relative extrema. 6 6. Find the absolute extrema of the function f(x) + over the interval (1,6]. I
Name: 1. For the function f(x) = x2 – 1 find and simplify: a. f(-2) b. f(-x) c. -f(x) d. f(x - 2) 2. Find the domain of each function below. Write your answer in interval notation. a. f(x) = x + 2 x2 + x - 6 b. 8(x) = (2x - 1 1 f(x + h) - f(x) 3. For the function f(x) = 2x2 – 3, find the difference quotient h 4. Use the graph of the...
11. As a general overview, these are the details one needs to look for when sketching curves (in no particular order: a Domain and range f. Relative extrema (maximum and minimum b. x-and y-intercepts values) c. Vertical asymptotes 9. Absolute extrema (maximum and minimum d. End behavior (including horizontal or values) polynomial asymptotes) h. Intervals of concavity e Intervals of increasing and decreasing i. Points of inflection behavior j. Other points of interest (corners, cusps, vertical tangents, discontinuities, etc) x3-3x...
find an equation of the tangent plane and parametric equations
of the normal line to the surface at the given point
z=-9+4x-6y-x^2-y^2 (2,-3,4)
Find the relative extrema. A) f(x, y) = x3-3xyザ B) f(x, y)=xy +-+-
Find the relative extrema. A) f(x, y) = x3-3xyザ B) f(x, y)=xy +-+-
The function f is defined as follows. f(x)- 4x-3 if x21 (a) Find the domain of the function. (b) Locate any intercepts. (c) Graph the function. (d) Based on the graph, find the range. (e) Is f continuous on its domain?
The function f is defined as follows. f(x)- 4x-3 if x21 (a) Find the domain of the function. (b) Locate any intercepts. (c) Graph the function. (d) Based on the graph, find the range. (e) Is f continuous on...
A Guide to Curve Sketching 1. Determine the domain of f. 2. Find the x- and y-intercepts off.* 3. Determine the behavior of f for large absolute values of x. 4. Find all horizontal and vertical asymptotes of the graph of f. 5. Determine the intervals where f is increasing and where f is decreasing, 6. Find the relative extrema of f. 7. Determine the concavity of the graph of f. 8. Find the inflection points of f. 9. Plot...
1. Consider the curve given by the function f(x) = -4.83 27(x + 1)2 You are given that -4x²(x +3) - 8.1 f'(x) = and f"(x) = 27(x + 1)3 9(x + 1)4 Compile the following information about f(x) and its graph. Show your work to justify your answers to parts (f), (g), (h), (i) and (j). Otherwise, give answers only. Answer "NONE” if the function does not display a feature listed. 1] (a) Domain of f (b) x and...
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