Given these data Estimate f(2.5) and f(4) using cubic splines. Plot the data along with all curves.

Q: Find the point "P" on the graph of the function y=sqrtx closest to the point (10,0)  The x…

A: Let the point is (x,y)= (x,sqrt(x))Distance of (x,sqrt(x)) from (0,0) is D

Q: Find the inflection point of the curve f(x)=2x³ – 18x²+ 30x. О а.3 O b. 3/2 С. 9 O d. None

A: We have to find out point of inflection

Q: This function has: 1) A y intercept at the point 2) x intercepts at the point(s)

A: Given,  fx=2x2+11x+123x2+10x+3 The x-intercept, y-intercept, and vertical asymptotes are to be…

Q: Examine the following functions for maxima-minima and trace the curve a. Y=x* + 1 a?x b. Y= a² –x²

A:

Q: The function f(x) = 4ᴫx3/3 describes the volume, f(x), of a sphere of radius x inches. If the radius…

A: f(x) = 4πx33 Volume of sphere , f(x) = 4πx33 where,  x is the radius of sphere in inches.…

Q: The slope of the secant line of the square root function at x=4 and x=9 is [a], and the y-coordinate…

A:

Q: Suppose that f is a linear function with slope 4 and that f(4) = 5. Find the equation for f. %3D…

A: Given query is to find the

Q: Find the area of a triangle bounded by the y-axis, the line f(x)=10−2x, and the line perpendicular…

A: y=10-2x here coefficient of x is -2 so the slope of the line is m=-2 and the perpendicular line…

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 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: Suppose the slope of the curve y = f'(x) at (4, 7) is §. Find f'(7).

A: Given slope of the curve y=f-1(x) at (4,7) is 45

Q: The range of function y=(x² – 1) is

A: on solving this we get the

Q: Given the function​ f, find the slope of the line tangent to the graph of f-1 at the specified point…

A: Obtain the inverse of the given function as follows:

Q: The slope of the line tangent to the graph of f(x) = 12 – 2x? at the point x = -9 4 9.

A: Solution

Q: Given the function g(x) = -x² + 6x + 15, determine the average rate of change of the function over…

A: The average of a function over an interval is given by . The given function is and the interval…

Q: Use the linear approximation to estimate the value. Compare with the value given by a calculator.…

A: Think of 4.19.9 as a value of fx,y=xy f4.1, 7.9=4.17.9 Then it makes sense to use the linear…

Q: Consider the function y = 1 2r2

A: To find: The horizontal and vertical asymptotes of fx. Given: The function is fx=2xx2-1. Concept…

Q: What is the equation for g(x) ?

A: The answer is option (A)  g(x)=x+5

Q: 1. Plot the function f(t)= (x+5) for -35 x 3. 4+3x2

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: For Exercise, identify the location and value of any relative maxima or minima of the function. 2 y…

A: A relative maximum is a point where a curve goes from increasing to decreasing.  A relative minimum…

Q: The cube root parent function y = Vx has been transformed a) 2.

A: given graph

Q: Use the graph of the function f to find approximations of the given values. y 4-

A: To find the values of f at x= a,  we imagine the vertical line x=a and where the vertical line…

Q: The height (in feet) of a stone thrown upward on another planet is given by the function f (t) =…

A:

Q: Find the slope of the secant line between x=−1 and x=2 on the graph of the function f(x)=−2x3 +3.

A: Given lines are x = –1 and x = 2. Given function is

Q: Find an equation for the line tangent to the graph of  f(x) = 6xex at the point (a,f(a)) for a =3

A: To write down the equation of the tangent to the curve at the given point

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 slope of the secant line between x=−1 and x=2 on the graph of the function f(x)=x3−4x2+5x.…

A: The slope of the secant line between x = −1 and x = 2 on the graph of the function f(x) = x3 − 4x2 +…

Q: 1. Plot the function f(t): (x+5) for -35 x 5. 4+3x2

A: Plotting graph by finding slope.

Q: Define h(x)= x3-x2-9x+9  Find the positive x value for which the slope is equal to 1.

A: Given that Define h(x)= x3-x2-9x+9  Find the positive x value for which the slope is equal to 1.

Q: Find the points on the graph of the function f that are closest to the point (a, b) by minimizing…

A:

Q: The height of an arch above the ground is given by the function y=10sinx, for 0 <= x<= pi .…

A: The given interval is [0,π] So, a=0, b= π

Q: find the linear function with the following properties: f(1)=5 slope of f=6

A: Given : f(1)=5 slope of f = 6   To find : linear function satisfying above properties

Q: Determine the value of x when the slope is its maximum for the function f(x)=2cos(3x)

A:

Q: The distance traveled by a rocket (in feet) after launch is given by the function f (t) = -16t? + 1,…

A: Given query is to find the velocity after 15 second.

Q: Find the range of the function y =1+ x2

A: Introduction :

Q: Find the slope of the line that connects the points x = a and x = a + h for f(x) = 2x^2

A: Given,        The slope of the line that connects the points x=a and x=a+h for fx=2x2.

Q: Find the slope of the line tangent to the graph of f(x) = -1₂ at x = 3. x+2 Provide your answer…

A:

Q: Find the slope of the secant line between x = -1 and x = 2 on the graph of the function f(x) = 5x° –…

A: Given function is f(x)=5x3-5x2+2x+3

Q: Consider the function f(x)=(x+1)(x–1)2, At what value of x will the graph of f cross the y-axis?…

A:

Q: For which values of x does the graph of  f(x) = 8x3 - 12x2 - 24 have a horizontal tangent? Enter…

A:

Q: Use the graph of f(x) = [[x]] to graph the indicated function. y = [[2x]]

A: Given function is: y=[[2x]] It is greatest integer function. Given basic function is: fx=[[x]]

Q: Find the slope of f(x) = In(6x) at (2, 2.48). Use a graphing utility and round to the nearest…

A: Given: fx=ln6x To determine:  Slope of the given function at 2, 2.48

Q: 1. Plot the function f(t) = (x+5) %3D 4+3x2 for -35 x 5.

A:

Q: The elevation of a path is given by f(x) = x^3 - 5x^2 + 30, measured in feet, where x measures…

A: The elevation as a function of path is given below.

Q: Determine the value of x when the slope is its maximum for the function f(x) = 2cos (3x)

A: Given,  f(x)=2 cos(3x)

Q: . Determine the value of x when the slope is its maximum for the function f(x) = 2cos (3x)

A: Here we have to use the concept of derivatives.

Q: Find the slope of the secant line between x = -2 and x = 3 on the graph of the function f(x) = -2x2…

A:

Q: At what point (x, y) is the function f(x) = 6x - 6 closest to the origin? Enter an exact answer.…

A:

Q: Find the curve length of the function 1 1. f(x) = ;x² 0 < x < 3

A: We can find the curve length as below.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.