Let A(x) be the function defined by A(x) = 4 We have A(0) = -3 A'(-1/2) = -2 for x = [-1,0], A(x) = 2 -3 2 3 -1 4 f(t)dt, where f is the function whose graph is shown. 5 A(3) = A' (3) = for x = [0, 4], A(x) =

Q: Consider the function f (x) = 6x² + 4x + 2. Find F(x) so that F' (x) = f(x). %3|

A: f(x)=6x2+4x+2To find: F(x) such that F'(x)=f(x)

Q: Find y as a function of a if y(0) = 7, y/(0) = -12, y'(0) = 108. y(x) = y" + 36y' = 0,

A:

Q: Find y as a real-valued function of tif y(5) 9, y'(5) = 9. = y = 49y" 140y + 100y = 0, -

A:

Q: For the function f(x) = -7 e X, find f"(x), f''(0), f'"(9), and f''(-9). f"(x) = (Type an exact…

A: The objective is to solve the above question.

Q: find the function f(x) if f'(x)=(2/1+x2)+(5/7)x5/7 and f(0)=2

A: Given, f'(x)=(2/(1+x2))+(5/7)x5/7

Q: 1.2 s Find first derivative for the following functions. dx (a) y = 5+ 6x + 4x3 (b) y = In(2x) +x*…

A: Note:-Since you have asked multiple questions, we will solve the first question with three sub-parts…

Q: (b) A poll commissioned by a politician estimates thatt days after he makes a statement denegrating…

A: Given: Percentage of constituency that supports a politician is: St=75t2-3t+25t2+3t+25 Derivative of…

Q: 2. Determine f'(1) for the function f(x) = (8x – 6Vx5 + 3) (x² – 9x² +) -

A: A detailed solution is given below

Q: Find the DERIVATIVE of the following functions using Rules for Differentiating Algebraic Forms. Show…

A:

Q: If the function f(x) is defined as f(x) = = (4-2√√x)² √x -,x>0 Then, what is the value of ƒ'(16) = ?

A:

Q: 2. Find the derivative of f'(x) if ƒ(x) = x*+3x-V x2+x

A:

Q: Your used Chevy’s gas mileage (in miles per gallon) is given as a function M(s) of speed s in miles…

A:

Q: Find f. (x+ 1) (b) f'(x) = f(1) = 5 3.

A:

Q: Find y as a function of t if 5184y" – 1584y + 121y = 0, - y(0) = 6, y'(0) = 3. y =

A: We have to find the general solution of the given problem.

Q: The derivative of the function f is given by f'(x) = - 2(x - 3)-3. Find an equation of the line to…

A:

Q: 6. Show that (an)neN C R is bounded if and only if lim supn→∞ an < +∞o.

A: To Prove:  ann is bounded sequence if and only if limsupan&lt;+∞.

Q: s of stick t

A: Given that it needs 5meters of stick to make a picture frame.

Q: If f(x) = 6 + 5x – 5a, find f'(- 3).

A: Topic = Derivative

Q: f(x) 132. Let h (x) = g(x) Find a. h' (1), b. h' (3) , and с. h' (4).

A: Given

Q: 2. Find the derivative of each of the following functions: y = x¹2 (i) (ii) (iii) (iv) y = 3x ¹ y =…

A: 1) y=x12Differentiate w.r.t.'x'dydx=ddx(x12)We know thatddx(xn)=nxn-1Thereforedydx=12x11

Q: 2. Determine the exact value of f'(2) for f(x) = (2e³ + 3e-6x)5.4,

A:

Q: If f(x) = x' – 8x + 2, find f (-4).

A: We have,  fx=x3-8x+2           ⋯⋯1

Q: Given f(x) = x + 4, x < 0. Find (f-1)' (5) 10 1 2 | 29

A:

Q: Which of the following is the second derivative of f(x) = 2x - 6x2 + 5x - 9? Select one: a. f"(x) =…

A: We are given with the function and we have to find the second derivative for which we have to…

Q: Find y as a function of if y(0) = 19, y'(0) = 19, y"(0) = 4, y"(0) = 0. y(x) = y(4) 4y" + 4y = 0,

A: y(4)−4y′′′+4y′′=0y(0)=19,y′(0)=19,y′′(0)=4,y′′′(0)=0

Q: Find y as a function of a if y(0) = -2, (0) = 9, '(0) = -62. y(x) = y" - 4y" -y + 4y = 0,

A: Given that y''' -4y'' - y' + 4y = 0 ,   y(0) = - 2 y(0) = 9 '(0) = -62.

Q: Find f′(x) if f(x) = lnx / x2

A:

Q: Let y= f (x) be a function with f (4)=12 and f(4)= 0.5.

A: We have to find

Q: Compute f'(a) algebraically for the given value of a. f (x) 2x – a2; a = -1 limp 0 (4 – h) = 0 limp…

A: The function is given by f(x) = 2x-x2; a =-1 To evaluate : f'(a) Formula Used : f'(a) = limh→0f(a+h)…