Show that a constant function f(x) = b has an average rate of change of 0. Compute the average rate of change of y = V4 - x on the interval [-2, 2]. Explain how this can happen.

Q: Find the average rate of change of f(x) tan x from to

A: f(x)=tan x

Q: Determine the instantaneous rate of change of the function πt ³ √x sin 2 f(x) = LV x3 1 + √t at x=2.…

A: Leibnitz integral rule.

Q: Find the maximum rate of change of f(x,y)= e^x^2 at (3,0) and the direction in which it occurs.

A: GIVEN DATA : Function fx,y=ex2        TO FIND : Maximum rate of change at 3,0 and the direction  The…

Q: Find the average rate of change for function over the given interval.

A: Given  y=3x-2.

Q: What is the average rate of change of the function f ( x ) = 3 x over the interval [ 2 , 5 ]

A:

Q: What is the average rate of change of the function f(t) = -3t between t--4 and f--3?

A: what is average rate of change of the function f(t)=t2 -3t between t=-4 and t=-3   answer  put t=-4…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: Given,

Q: z = Vx4 + yf, fz (1, 2)

A:

Q: Find the maximum rate of change of f(x,y) =x²y+ /y at the point (1,1). In what direction does it…

A:

Q: Find maximum rate of change of f at the given point. f(x,y)=sin(xy), (1,0)

A:

Q: Find the third derivative of ƒ (z) = VT2z+I. f" (z) =

A: We use the exponent rule and chain rule.

Q: Find the derivative of the function. 2x F(x) = arctan(t) dt Vx F'(x) : %D

A: The given problem is to find the derivative of the given definite integral function. We have to use…

Q: Find the maximum rate of change of f (x, y) = xy ^ 2 + root (y) at the point (2,1). in which…

A: The maximum rate of change of f(x, y) happens along the direction grad(f) at the given point (2, 1).…

Q: Find the maximum rate of change of f (x, y) = xln /x2 + y2 at (1,2) and direction in which it…

A: To find the maximum rate of change of fx,y=xlnx2+y2 at 1,2 and direction in which it occurs.  First,…

Q: Let f:[-n, 7] –→ R, where f(x) = 2 sin (2x) – 1. TC Calculate the average rate of change of f…

A:

Q: . What is the average rate of change of the function g(t) over the interval from t=atot=b? How is it…

A: Suppose gt be a function defined on the interval a , b Then, the average rate of change of the…

Q: Find the average rate of change of f from 0 toπ/2 . f(x)=sin( x/2)

A: Derivative of a function determines the change of one variable with respect to another variable.…

Q: Find the average rate of change of f(x) = x2 + 3x + 1from 1 to 2. Use this result to find the…

A: Average rate of change of a function f(x) is calculated as the total change in the function divided…

Q: Find the total derivative of V with respect to X

A: As the differentiation is with respect to x, x becomes the variable. y and z becomes constants

Q: Find the average velocity of the function over the given interval. y= - 3x? - x, [5,6] – X,

A:

Q: What is the average rate of change of the function g(t) over the interval from t = a to t = b? How…

A: The average rate of change of the function g(t) over the interval from t = a to t = b is given by:…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs…

A: Consider the function: fx,y,z=xlnyz Differentiating with respect to “x” then,…

Q: find the average rate of change of the function overthe given interval or intervals. g(t) = 2 + cos…

A: Given, g(t)=2+cost, -π,π The average rate of change of function f(x) over an interval [a,b] is,…

Q: 5. First compute the derivative of f(x)= Vĩ and then use it to: a. Find the equation of the tangent…

A: Given equation of curve is fx=x. Power rule of differentiation states that: ddxxn=nxn-1…

Q: What is the difference between the linearization, L(x), of f at a, and the linear approximation (or…

A: Given question:- What is the difference between the linearization, L(x), of f at a, and the linear…

Q: The average rate of change of the function y = x² in the interval 2 sx< 5 is %3D

A:

Q: Find the magnitude of the greatest rate of change of f(x, y, z) = (x2 + z2)3 at (1, 3, -2), and…

A: Consider the provided question,

Q: The maximum rate of change at a point on a function f(x,y,z) is да ylgr

A:

Q: The average rate of change of fx) = ax' Over the interval osxs1 IS a

A:

Q: Let f(x, y) = xe". What is the maximum rate of change of f at the point (2,0)?

A:

Q: find the average rate of change of the function overthe given interval or intervals. g(t) = 2 + cos…

A: gt=2+cost,  0, π

Q: Find the derivative of the function f(x,y) = tan at the point (3, - 3) in the direction in which the…

A:

Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 7y + 3z) at the point (– 2, – 3, – 6). - -

A:

Q: Find the derivative of the function. F(x) = et dt F'(x) = %3D

A: We know that by Leibniz rule of differentiation under integral sign, we have

Q: What is the average rate of change of f(X)= X2-2 on the interval [-1,3]?

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A:

Q: What is an average rate of change of function f(x) over the interval [1, 6]?

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: The average rate of change of the function f(z) = 13z +4 on the interval [1, 4] is

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. (x, Y)…

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: Show that the average rate of change of the linear function f(x) = a over any interval say [x1,x2]…

A:

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

A: Find the total derivative

Q: Find the gradient of the tangent to the curve xy“ + y+ ( log_(x – 2))² = 14 at the point (3, 2).

A:

Q: Find the average rate of change of the function f(x)=x2  on the interval [x, x+h]

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. F(x,…

A: SOLUTION-

Q: Estimate the true percent relative error for the first derivative of the function, y =[e!n(x)72, at…

A: We can solve this using Central difference formula f'(x) = (f(x+h) - f(x-h))/(2h)     x 0.95 1…

Q: Let f(x)= 2x^3+3x^2-12x on [1,3] What is the average rate of change in f on [1,3]?

A:

Q: DETERMINE THE INSTANTANEOUS RATE OF CHANGE OF THE FUNCTION AT X=1 sin (2³) 1 + √t - f(x) = x3 dt

A: