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Graphs and Functions

Graphing and Tangents

A) Graph b) Draw tangent to graph @ points where x coord. are -2, 0, and 1 c) f(x) by determining Limit h>0 f^'(x+h) - f(x) / h d) f^' (-2), f^' (0), and f^' (1) (should meet slopes in part b) f(x) = 1/2 x^2

Graphs and Linear Equations

1. The following table shows the height of a tree as it ages. In Excel, plot each point on the same graph where the first coordinate is the age of the tree and the second coordinate is the height of the tree (age, height). After plotting each point, explain if there is a linear relationship between the age and height of the tr

Graphs and Limits

Graph each function then find specified limits. Exist? f(x)=x^2 ; Find lim x--> -1 f(x) and lim x--->0 f(x)

Parallel Lines

Suppose the government mandated gasoline prices to remain constant at $4.26 per gallon everywhere across the country, restricting gas stations from increasing the price in the future. The law will take effect in 2012. Is there an equation that would illustrate the price of gas under the new law? Is there an equation that i

Question About Plotting a Function

Find the intercepts, slope, asymptotes, relative maxima and minima, and intervals of increase or decrease of the function and plot it. f(x) = x^4 + 2x^3

Find an equation of the tangent line to the graph.

Find an equation of the tangent line to the graph of the relation given by x2 - xy + y2 = 7 at the point (2, 3) . x + 4y - 14 = 0 4x + y - 11 = 0 11x + 4y - 34 = 0 7x + 3y - 23 = 0 17x + 8y - 58 = 0 none of these ∫ 3/x^2/5 dx = (15/2)x^

Equation for the tangent line to a graph.

Please choose the correct answer and indicate final answer. 11. f(x) = (x + 4)^1/2. An equation for the tangent line to the graph of f(x) at the point where x = 77 would be x - 6y + 13 = 0 x - 8y + 20 = 0 x - 10y + 29 = 0 x - 12y + 40 = 0 x - 14y + 53 = 0 x

Maximum Value of Functions

A jewelry floor safe with a square base is to be made so as to have a total volume of 648 cubic inches. The side material for the safe costs $1 per square inch. The material for the top costs $4 per square inch while the material for the bottom costs $2 per square inch. What, in inches, would be the height of the most economical

Points of Inflection

Find the x-coordinate of the points of inflection of f(x) = 47 + 13x + 18x^ 2 + 4x^ 3 - x^ 4 -3, 1 -1, 3 -3, -1 1, 3 -4, -1 1, 4 -4,1 -1, 4 none of these

Slope Predictor Formula and limits

See attached file for full problem description. 1. Apply the slope predictor formula to find the slope of the line tangent to y = f(x) = (2x + 4)^2 - (2x -4)^2. Then write the equation of the line tangent to the graph of f at the point (3, f(3)). 2. Find all points on the curve y = (x+4)(x-5) at which the tangent line is horiz

Solving Equations and Graphing

(u+23)^ 1/2 = 9 Graph 22) y =0.3x Since any real number can be used in place of x in y = 0.3x the domain is (-oo, oo) Since any real number can be used in place of y in y = 0.3x the range is (-oo, oo)

Graphing a Line

Please show work for a full understanding, thanks Graph f(x) = 3x + 2

Is a Series a Function?

Using the index "n" of the partial sums of a series as the domain, and the value of the corresponding partial sums of the series "Sn" as the range, is a series a function?

Slope-Intercept Form of a Tangent Line

Write the slope-intercept form of an equation of the line tangent to the graph of g(x) = x^3 - 6x^2 + 5x + pi at its point of inflection. (^ means exponent)

Find the Equation for a Tangent Line

Please explain the steps and solution, thanks: Find an equation of the line tangent to the curve defined by the equation at the specified point: x^2/3 + y^2/3 = 2; (1,1) (^means exponent and 2/3 is the exponent)

Functions : Areas of Increase and Decrease and Extrema

Please explain and express the answer exactly, for example √3 rather than in decimal form, thanks: s(t) = -8t^9 + 9t^8 - 7 (a) Where is the function increasing? (b) Where is the function decreasing? (c) Where does the function have local maxima? (d) Where does the function have local minima? (^ means expone

Ordered Pairs

Complete the ordered pairs for the equation y = 7x + 7. (?,0), (3/7,?), (0,?), (-3/7,?)

Interval notation

Write the sets attached using interval notation. If the set is empty, write O