Find the average value of the function f(x) = x3 - 6x2 + 15 between x = 1 and x = 3.

Q: Find absolute maxima and minima of the function f(x; y) = x^2 + y^2 on the closed triangular plate…

A: The points are:

Q: Find linearization of the function f(x) = Vx + 3 at a = 1 and use it to approximate V3.98

A:

Q: Find the equation of the normal line (NL) to the graph f(x)=x³ – 4x atx = 3 .

A: We need to find derivative.

Q: Given f (x,y) = x³ + y3 – 3y² – 3x² – 9y, find the critical points and use the Second Derivative…

A: solution :-

Q: Find the linearization L(x) to the function f(x)= Vx+4 at x =4, then use the linearization to…

A: linearlization of f(x) at x=a is  L(x) = f(a) + (x-a)f'a)

Q: Find positive numbers x and y, whose sum is 75, such that xy2 is maximized.

A: Positive numbers x and y,x+y=75xy2 is maximized

Q: Use the second derivative test to identify any critical point and determine what each critical point…

A: Critical point: The point where the function fx, y is defined and its gradient is a zero vector or…

Q: Find the best linear approximation to f(x) = x² on the interval [0, 2].

A: Here we use Taylor's approximation.

Q: Find the relative extrema using both the first and second derivative tests. f(r) = 2x³ – 9x² + 12x.…

A: Consider: fx=2x3-9x2+12x. Critical point is the point where the derivative of the function is either…

Q: Given the function f(x) = (x-2)2 + (y-3)2 (i) Find the critical points. (ii) Using the second…

A: The given function is: f(x,y)=(x-2)2+(y-3)2

Q: Approximate X f(x) = e*over the interval [- 4, – 2] using 2 subintervals.

A: In this problem, Simpson 1/3rd rule is used to find the approximate value of e^x over the interval…

Q: Find the equation of the normal line in the curve x2 − 6x + 2y − 8 = 0 at x = 3

A: We need to find equation of normal line.

Q: Find the local linear approximation L (x)of the function f (x)= x² +3 at x = 1

A: Given that: f(x)=x2+3

Q: Find the antiderivative of f(x). f(x) = 3e6x+ sec2(x) +x3

A:

Q: What is the linear approximation of the function f (x) = e x at x = 1?

A:

Q: Use differentials to approximate V36.1. 3.

A: Consider y = root x.Let take x = 36 and delta x = 0.1.Find delta y as follows.

Q: Determine the average rate of change of f(x)=2x+1 on the interval 4<x<5. a) f Ax b) Af Ax = 2 O d) 4…

A:

Q: Find the linear approximation to f(x) = at a = 4.

A:

Q: Find an antiderivative of the function f(x)=1/x4.

A:

Q: Find the linear approximation of f(x) = (5 + x)n at x = 0. Use the approximation to estimate the…

A: fx=5+xn at x=0. Differentiating with respect to x, we get f'x=n5+xn-1 Now, f0=5+0n=5n &amp;…

Q: Find f(x), the most general antiderivative of the function: f' (x) = 3x –

A:

Q: Estimate the slope f'(3.5) for f (x) = sin(3x) using: a. Forward difference approximation with h =…

A: f(x)= sin3x x y y1 y2 y3 y4 3.3 -0.1557             -0.193       3.5 -0.3507   0.0139…

Q: Find the marginal revenue function. R(x) = 7x – 0.05x² R'(x) =

A:

Q: Find the average vale ot f(x)=Dx²e-2x overthe interval [-1,1]

A:

Q: Find the linearization of the function f (x) = x° at z = 1.

A: Given, f(x)=x6

Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) L(x) =

A:

Q: Find an antiderivative F(x) of f(x) = 7x – Vx.

A:

Q: Find the critical point of the function. Then use the Second Derivative Test to determine whether it…

A:

Q: Find the differential of the function.

A: Differentials are infinitely small quantities. We usually write differentials dx, dy, dt (and so…

Q: Estimate Af using the Linear Approximation and use a calculator to compute both the error and the…

A: Given by,fx=3+x  , a=1 , ∆x=0.1 find out the value of ∆f≈

Q: The total derivative of f(x,y )=3 x+ 3 y-41n y is

A: Given function is fx,y=3x3+3y2-4 ln y find the total derivative  dz=fxx,ydx+fyx,ydy

Q: A total cost function (in dollars) is given by C(x) = 116 + 3x + 0.37x. Use differentials to…

A:

Q: Find the linear approximation L(x)of f(x)=x^4 at the point a = −5 L(x)=

A: Given that f(x) = x4 We have to find the linear approximation L(x) of f(x)=x4 at the point a= -5.

Q: Find the maximum and minimum value of f (x,y) =x' + 3xy² – 3x² – 3y² +4 = X" - -

A:

Q: 42. f(x) = sec² x, [

A:

Q: Find the linear approximation of f(x) = Vx-1 approximate 2.02. near a = 2. Use the result to

A:

Q: For the cost function C(x)=300+10x+0.03x^2, show that average costs are minimized at the x value…

A: Given data: The expression for the cost function is C(x)=300+10x+0.03x2.   The expression for the…

Q: Find absolute maxima and minima of the function f(x;y) = x^2 +y^2 on the closed triangular plate…

A:

Q: Find the average rate of change of the function f(x) = 2x- 4x 8, on the interval r E [-3,2]. |3D

A:

Q: Find the marginal revenue function. R(x) = 3x-0.05x2 R'(x)=

A:

Q: Find the antiderivative of the function: f(x) = ex + 3x - x2

A:

Q: Find the average rate of change of the function on the interval specified Y=1/x on [1,3]

A: We know that ,The average rate of change of function over an interval a,bis given by f(b)-f(a)b-a

Q: The average revenue is defined as the function R(x) Ř(z) (x > 0) Prove that if a revenue function…

A: Let Rx denotes the revenue function. The average revenue function is defined by Rx=Rxx where x&gt;0.…

Q: The total derivative of the function f(x, y) =3x'y- xy is

A: Find the total derivative

Q: Find constants c1 and c2 such that F(x) = c1xe -x + c2e -x is an antiderivative of f(x) = 3xe -x .

A: Given: Fx=C1xe-x+C2e-x  and fx=3xe-x

Q: Find L(x) (Linearization function), given f(x) = ev2x at the value a = 2.

A: