Let P = (x,y) be a point on the graph of y = x- 12. %3! Express the distance, d, from P to the origin as a function of the point's x-coordinate.

Q: Find the slope of the secant line to the function f(x)=4x²- 3x, through point P, where x= - 1, and…

A: To find the slope of secant line PQ to  the function f(x)

Q: Find the length of the curve of the graph of the indicated function. y = (x + 3)3/2, between points…

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Q: Find the area of a triangle bounded by the y axis, the line f(x) = 4 – 3 x, and the line…

A: Given: f(x)=4-13x If the given line is y=mx+c with slope m then the slope of a line perpendicular to…

Q: Make two separate plots of the function f(x) = (x+ 1)(x-2)(2x-0.25)- e. 2. one plot for 0sxs3 and…

A: Given, f(x)=(x+1)(x-2)(2x-0.25)-ex We plot this function in two different intervals.

Q: Find the mean value of the function y = 4cos x on the interval 0,

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Q: Find the area of a triangle bounded by the y axis, the line f(x) = 5 – -x, and the line…

A: Given data:     The expression of the first equation of the line is: f(x)=5-2x/3. The second…

Q: Find the intervals on which the function y=xx(x>0) is increasing and decreasing.

A: We take ln on both sides of the function

Q: Find the point P on the graph of the function y=sqrtx closest to the point (9,0) The x coordinate of…

A: We have to find the point P on the graph of the function y=x closest to the point (9,0). Also, find…

Q: b) Find the slope of the function f(x) = VI+1at point (15,4).

A: The slope of  f(x) at a point (a,b) or x=a and f(a)=b is given by, df(x)dxx=a or f'(a)

Q: What is the instantaneous slope of Y -5 at X = 5? o 1 O -1

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Q: -Which of the functions below has a range of y<-2?

A: Idea: Construct the line y = -2. If the graph remains below the line y = -2 then the function have…

Q: Find the equation of the line that is tanget to f(x)= 1/x at the point (2,1/2).

A: We need to find the equation of the line that is tangent to f(x) = 1/x at the point (2,1/2).

Q: Find the slope of the tngent line to the graph of the given function at the given Value of X.…

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Q: Sketch the graph and show all relative extrema and inflection points. y = 12x - x3

A: Topic:- function and application of derivatives

Q: Sketch the graph of the function. f(x, v) = y? + 7

A:

Q: Find the area of a triangle bounded by the y axis, the line f(x)=9−2/5x, and the line perpendicular…

A: fx=9-25x Comparing with fx=mx+c, we get m=slope=-25c=y-intercept=9 Therefore the slope of a line…

Q: Find the intersection  point of f (y) with x-axis.

A: Given the function f(y) .We need to find the point of intersection of f(y) with x-axis.

Q: Find the area of a triangle bounded by the y axis, the line f(x) = 10 T, and the line perpendicular…

A:

Q: Determine the point(s) at which the graph of -8x f(x) 2x - 1 has a horizontal tangent. (x, y) = Need…

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Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = Inx?;…

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Q: determine the slope function S(x) for f(x)= lxl

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Q: What is meant by “the value of a function at x”?

A: Let the function be f(x).

Q: The Range Rf for the functionf (x) = tanhx is:

A: Range of f(x)= tanh x

Q: Graph the functions in excercise

A: Given function, y=x-13-1

Q: The level curves of the function f (x, y) = V2x2 + y? – 1 are

A: Please refer to the image below

Q: Use the graph 70 on the right to evaluate S°f(x)dx

A: Consider the given graph: Divide the region in three parts: First is 0-20 Second is 20-50 Third is…

Q: Find the area of a triangle bounded by the y axis, the line f(x) = 10 1 and the line perpendicular…

A: A triangle bounded by the y axis, the line f(x)=10-13x, and the line perpendicularto f(x) that…

Q: Find the point on the graph of the function that is closest to the given point. f(x) = /x, (3, 0)…

A: Given, y = f(x) = x Let's assume the closest point to (3,0) will be (x, y) then (x,y) = (x, x)…

Q: Make two separate plots of the function f(x) = (x+1)(x-2)(2x - 0.25)- e one plot for 0sxs3 and one…

A: We need to make two separate plots of the function f(x)=x+1x-22x-0.25-ex one plot for 0≤x≤3 and one…

Q: The height of an arch above the ground is given by the function y=10sinx, for 0 less than or equal…

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Q: Sketch the level curves when z = 5 and z = 8 for the function z = z + y? + 4. Hence, sketch the 3D…

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Q: Find the area of a triangle bounded by the y axis, the line f(x)=8−1/3x, and the line perpendicular…

A: We have to find the area of a triangle bounded by the y axis, the line f(x)=8−13x, and the line…

Q: Based on the scatterplot predict the value of y when x = 30 -mittens 10

A: From the scatter diagram, the slope of the regression is downward slope   As slope is downward,…

Q: Find the area of a triangle bounded by the y axis, the line f(x)=8−13x, and the line perpendicular…

A: Recall : Area of the triangle with three points x1,y1,x2,y2 and x3,y3 :            A=…

Q: What is the equation of the function that is obtained from f (x) = | x | by reflecting about the x…

A: Given information:The given function is

Q: Find the slope of the curve given by f(x)=x3e4x at the point (-1,-e-4)

A:

Q: y = Va+1-3

A:

Q: 14х y = Зх-6

A: Given:   To determine: excluded x value for the function.

Q: Find the area of a triangle bounded by the y axis, the line f(x) = 6 and the line perpendicular to…

A:

Q: Find the point P on the graph of the function y=√x closest to the point (5,0) The x coordinate of P…

A: Since, we have to find a point P on the graph of the function y=x -(i) closest to the point…

Q: What is the output when the input is 4 for a linear function that has a y-intercept of 5 and a rate…

A: Given information: The input of the linear function is 4. The y-intercept of 5 and the rate of…

Q: Use the graph of f(x) above to estimate the value of f'(0) to one decimal place.

A: The graph of f(x) has a vertical tangent at the point (0,f(0)).

Q: The level curves of the function f (x, y) = /2x2 + y? – 1 are

A:

Q: The average change of the function y = √x from x = 4 to x =16 is _________________ ?

A: The given function y=sqrt(x). We need to find the average change of function over interval [4,16].

Q: Graph the function as a solid curve 1) f(x) =극지•3

A: We have to graph

Q: Find the average rate of change of f(x) = 6x? - 2 on the interval (3, a].

A:

Q: Find the average rate of change of f(x)=9x2−8 on the interval [4,b]. Your answer will be an…

A: Given function , f(x)=9x2-8 on the interval 4,bThe average rate of change of fx=9x2-8 is in…

Q: Find the average rate of change of f(x) = 3x2 - 5x from 1 to 3.

A: Given to evaluate the average rate of change of f(x) = 3x2 - 5x from 1 to 3.

Q: Differentiate the function.

A: Given: y=ex1-ex