The height of a ball t seconds after it is thrown upward from a height of 7 feet and with an initial velocity of 80 feet per second is ........ . ...... .... f (t) = -16 + 80t + 7. (a) Verify that f(2) = f(3). f (2) = |103 f(3) = 103 ft ft (b) According to Rolle's Theorem, what must be the velocity at some time in the interval (2, 3)? 3.5 ft/sec Find that time. t= 2.39

Q: b) Given h(x) = 3x² + 2x and f(x) =- Vx – 2, find (h • f) (x + 2)

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Q: 7. Find c such that f(c) = fave where fave is your answer to the previous problem.

A: (7) The function is given as , fx=x3 find c for fc=fave where fave is average value of f on 0,27.

Q: The function f(x) = = a) 0 b) 1 Oc) 2 d) 3 (x² + 1) (x² + 2) has how many x-intercepts?

A: Given function:- fx=x2+1x2+2

Q: ) = x² + y² - 8x - 6y subject to the

A: Given that fx,y=x2+y2-8x-6y. First we have to find the extreme point on the domain given in the…

Q: 3. Find f'(x) for f(x) = v5 + e2x xe2x-1 А. V5+e2x 1 2v2e2x С. 5+ e2x e2x D. V5+e2x V5+e2x B.

A: In this question, concept of chain differentiation is used in this question.

Q: The function f(x) = 2x? – 332? + 144x – 10 has two critical numbers. The smaller one is æ = and the…

A: Please refer the attached image for complete solution.

Q: Q2) Find the values of constants (a)&(b) that makes the f(x)= ax + b 3 (-3 x≤-2 -2<x<4 x24 Con

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Q: Find f(x) by solving the initial value problem s'(x) = 4x2-5, f(0) = -3 %3D

A:

Q: (f) What is the first-order condition implied by unconstrained maximization of I1 X 1333 X, where x…

A:

Q: The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per…

A: Given function f(p)=-50p2+1600p-11000 , where p is the price per shirt and f(p) is monthly profit…

Q: Find f′(x) and f′(c). Function f(x) = (2x2 − 3x)(9x + 4) Value of c = −1

A: f(x) = (2x2 − 3x)(9x + 4) c = −1   f'(x) = (2x2 − 3x).(9x + 4)' +  (2x2 − 3x)'. (9x + 4)        =…

Q: Find the particular solution determined by the initial condition. 2/3 f'(x) = 3x - 6x; f(1) = - 7…

A:

Q: x²–1 If f(x) and g(x) = Vx – 1, which will yield (f 0 g)(x)? %3D r2

A:

Q: Q1. Find ý of the function x2 – e2x+3y – In(xy³) = 0. -

A: here is the solution

Q: If S f(t)dt : 3x2 + 12x, what are the possible values of a? Verify that your values of a are…

A: The given integral relation is: ∫axf(t)dt=3x2+12x From the fundamental theorem of calculus,…

Q: 3 na of the function f(x) =x3 -x2 - 6x + 12, -3 < x< 3. 2

A: Solution of the problem as follows

Q: 1. Solve for the values of x in the function below. f(x)=x3-4x-0.5x2+2

A:

Q: Which is equal to () (x) given that g(x) = 1 – 3x and h(x) = Vx? %3D Vx – 3xVx 3xVx Option 1 Option…

A: Let's find.

Q: Find the value of a so that f(x)= x2 + a has a range of [-2, ∞).

A:

Q: Find f(x) by solving the initial value problem. f'(x)=3x2+4x-3; f(2)=4

A:

Q: 11b. Consider the function f(x)=5x* – 4x³ +4. Isƒconcave up or down at the point x = -0.2? A.

A:

Q: The function f(x) = 2x³ – 21x² + 60x – 7 has two critical values. The smaller one equals and the…

A: The given function is f(x)=2x3-21x2+60x-7

Q: [4 Let A = * 1. Find f (A), where f(x) = 2x3 + 3x2 + 4x + 5

A: Answer

Q: A once-popular children's doll is slowly declining in popularity. The quartic function f(x) = 0.002x…

A: Given that f(x)=0.002x4+0.025x3-0.364x2-7.243x+86.993 where x is the number of years since 1993 we…

Q: Express f(x) in the form a(x − h)2 + k. f(x) = −4x2 + 24x − 17   f(x)=?

A: Given: f(x) = −4x2 + 24x − 17…

Q: Find f by solving the initial-value problem. f'(x) = 9x² + 6x – 9; f(2) = 5 - f(x) %3D

A: Given,  f'x = 9x2+6x-9  f2 = 5  We have to find  fx

Q: The derivative of f(x)= (x2+2x)(x²-2x) is a. 4x3-8 O b. x-4x2 с. none d. 3.

A:

Q: The function f(x) =is 1-z2 Is 9+z2

A:

Q: 2 Given that f(x) = 4x – 7 and g(x) = 4 – a?, calculate (a) f(g(0))=| (b) g(f(0))=|

A: Answer(a): The given functions are: fx=4x-7 and gx=4-x2. Then, the composition function is given as:…

Q: (c) Find f-1. f-1(x) = X , x20

A: We plug f(x)=y then switch x and y. f(x)=x+4y=x+4x=y+4

Q: e. f(x) = 2* OA. O(x²) B. Q(x²) C. O(x²) В. f. f(x) = [x][x] (floor of x times ceiling of x) OA.…

A: Option (B) is the correct answer.

Q: Find f by solving the initial-value problem. f'(x) = 6x2 + 8x – 9; f(2) = 4 %3!

A:

Q: Find the function f(x) by solving the initial value p 3. 3x2 f'(x) = -(1, 1) 4

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

Q: Find f'(x) for f (x) = v5+ e2x

A: Given,          fx=5+e2x

Q: Express the follo lowest form +4 a 2 1-3x S+x

A:

Q: How do I find the possible inflection points of f(x)=a/((x^2)+(b^2))? It also states a and b are…

A: To find point of inflection we need to find x from f"(x)=0

Q: The General solution of f (x) is f(x)=- x 2x? + 2x+c with the initial condition f(1)=2,then 3 2 he…

A:

Q: Find the approximate value of f (3.02), where f(x) = 3x2 + 5x + 3.

A: Given

Q: Find f by solving the initial-value problem. f'(x) f(9) = 45

A:

Q: Find f by solving the initial-value problem. f '(x) =8/(x1/2), f(9) = 51

A:

Q: Find (f-1)'(a). f(x) = V 3x3 + 3x2 + 2x + 1, a = 3 (f-1)'(a) =

A: inverse function derivative

Q: Find the value of (A+ V)²(x² + x) with h=1.

A: To find the value of Δ+∇2x2+x with h=1.

Q: the total daily profit of a certain food company for the sale of boxes of buko is given by the…

A: Given that the profit function is: Px=-0.001x3+0.1x2+3x-300 Then we get,…

Q: The derivative of f(x) 4 (22 +17x) is O -4c (2a + 17) O -4r 2(2x + 17) O 4x + 68 O 4x 2(2x + 17) O 4

A: Here, it is given that f(x)=4x(x2+17x) We need to find the derivative of the function f(x).

Q: The fixed-points of f(x) = (x² + 2) a and

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Q: Find (f-1)'(a) for f(x) = V3x + 4 when a = 2. (Enter an exact answer.)

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Q: As dry air moves upward, it expands and, in so doing, cools at a rate of about 1°C for each…

A: Answer for the question will Start by writing the expression describing the value of temperature…

Q: 2 Find f4(x), given f(x) = 5x ° – 4x² – 2x+ 1 O A. 300x O B. 600x O C. 400x+8 O D. 400x´+8

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Q: Find (f-1)'(a) for f(x) = V4 – 3x when a = 1. (Enter an exact answer.)

A:

Q: If S. f(t)dt = 3x² + 12x, what are the possible values of a? Verify that your values of a are…

A:

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.