Find the average rate of change for f(x)=x+1f(x)=x+1 over the interval [4,5][4,5]. Be sure to simplify the answer.

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: Use differentials to approximate the change in y = f(x) from x = 4 to x = 4.1 for the function, f(x)…

A: It is given that,

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

A: Given  y=3x-2.

Q: Find the derivative of the function. f(x) = (x³ + s ]Inx O a. x*(1+Inx)+5 O b. x'(1+31nx)+ 5 O c…

A: We have to check

Q: Find the derivative of the function. f(x) = In(x + V7 + x²) f '(x) =

A:

Q: The derivative of y= xh* is O 1) (In x)(xh*-) O 2) 2 an x)(xh*) O 3) (In x)* O 4) xhx

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: Consider the function f(x, y) = y³ – 2y – x². Find the direc- tion of greatest increase at the point…

A:

Q: Find the average rate of change for the function over the given interval. y - 1 and x = 0 y%3D…

A: Givena function y = 5x + 7, between x = -1 and x = 0 Average rate of change for the function over…

Q: |If f(x) = a4 is the parent cubic function, prove that the AVERAGE rate of change of f(x) over the…

A:

Q: Find the derivative

A: The first derivative of f(x) is represented byf'(x) and the second derivative is represented by…

Q: Estimate the true percent relative error for the first derivative of the function, y =[eln)P, at x =…

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

Q: Find the linear approximation of f(x)=ln(x) x=1 and use it to estimate ln(1.1). L(x)= ln(1.1)=

A:

Q: When is f (t) increasing at the greatest rate?

A:

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

A:

Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate ln(1.33).

A: The linear approximation of f(x) at x=a is given by L(x)=f(a)+f'(a)(x−a) Given, f(x)=ln(x) at x=1.…

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: What formula will describe the average rate of change of f(x) = 3* over the interval [0, 3]? Don't…

A:

Q: Find the derivative of the function. f(z) = V - VE f '(x) =

A:

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 y with respect to over the interval [-1, 2] for the function y…

A:

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

A:

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

A:

Q: Find the first derivative or f'(x) of the function below using the techniques of integration f (x) =…

A:

Q: The derivative f'(a) represents the instantaneous rate of change of y = f (x) with respect to x when…

A: Given that we need to check  behaviour of  the statement " The derivative f'(a) represents the…

Q: Find the derivative of the function. 4 f(x) x In(x) f'(x) %D

A:

Q: Find the instantaneous rate of change of y =- at x = a

A:

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: 42. f(x) = sec² x, [

A:

Q: . Use a similar procedure to estimate the instantaneous rate of change of y = 3" at r = 0. Show your…

A:

Q: Find the average rate of change of the function over the given interval. y = V4x + 1; between x =0…

A:

Q: Find the average rate of change of the function over the given interval. Compare this average rate…

A: Average rate of change: Average rate of change of any function f(x) of [a, b] is, fave=fb-fab-a…

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

A: First find gradient and take magnitude for max rate of change

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: Find the derivative of the function. F(x) etd dt F'(x) =

A:

Q: Find the derivative of the function 4/ f f(x) = V (x – 3) at x = 2. f'(2) =

A: fx=x2-354⇒fx=x2-354 Differentiating with respect to x, we get f'x=ddxx2-354=54x2-354-1·dx2-3dx…

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: 1. F(x) = S, t³ - 5t dt

A:

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

A: Find the total derivative

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: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of df-1 at x = 1. dx

A: We have given function;

Q: Calculate the derivative of the function g(x)=x∫√x(t2−t)dt at x=1.

A: using the fundamental theorem of calculus we find g'(x)

Q: Find the average rate of change of the function f(x) = x 5x - 1, over the interval [-1,3

A: