Higher Order Derivatives Uses: acceleration, concavity Position: s (t) Second Derivative: Velocity: v (t) = s' (t) %3D d ( dy dæ ( dæ dy also f", y" dæ? Acceleration: a (t) = v' (t) = s" (t) 1. The height in feet at any time t (in seconds) of a particle thrown vertically is h (t) = –16t² + 256t. a. Find the particle's average velocity for the first 3 second of travel. b. How fast is the particle traveling 6 seconds after it is thrown and how high is it? c. When does the article reach its maximum height and what is that maximum height? d. What is the acceleration of the particle at t = 5 seconds?

Q: A particle moves according to the equation s(t) = 6 - , t > 0. Find its acceleration at time t.…

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Q: =記 う f6)2iぜsintdt b) f(x) = j sint? dt

A: Solution:-

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x2-3x)3 1. у 3 ; d'y/dx

A: Question 1,Given,            y=x2-3x3xTo find : d3ydx3

Q: Figure 1 below is a sketch of a function g(x) and its tangent line at the point (2,5). (2,5) → gex)…

A: From given graph g(2) = 5 g(3) = 0

Q: funchoN f whose second derivative is f ")= 5x+2sin(x If fo 3 and fro)= 3. what is fe?

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Q: Q4: Find the derivative of the function at P. in the direction of A 2) g(x, y) = x - (y² /x)+ J3…

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Q: using implicit differentiation. dx Consider the curve y° + y + 3x = 5. Find the derivative da Using…

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Q: bilowing equation f (x,y) = X<y. Find the derivative of f in the direction of (1, 2) at the point…

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Q: A particle moves along a line with velocity function v(t) = t2 – t, where v is measured in meters…

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Q: yx  = xy + xlny      for the function given as dy/dx Find its derivative. (x,y) = (1,e2)    What is…

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Q: S ize Find an equation of the line tangent to the curve defined by x + 5xy + y² = 7 at the point (1,…

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Q: PLS HELP ASAP ON ALL ASKED QUESTIONS. THIS IS TRUE OR FALSE

A: 11. TRUE 12. TRUEExplanation:Approach to solving the question: Detailed explanation:

Q: True or False The velocity of a particle whose position at time t is s(t) is the derivative s′(t).

A: Our Aim is to tell whether the statement the velocity of a particle whoseposition at time t is s(t)…

Q: Suppose an equation of the tangent line to the curve y = f(x) at the point where a = 4 is y = 8x –…

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Q: Pls help ASAP. Pls show all work.

A: Given, y=14 Aim : Find derivative

Q: Find the directional derivative of fix, y) = sin(y) at the point P (1.5) in the direction

A: Given f(x, y)=ex sin(y) and point is P(1,π2)   To Find: Directional derivative of f(x, y) at the…

Q: 19. y = tanh(e*)

A: Given; y=tanh(ex).

Q: estion 5 If f(x) = 1 du, then what is f'(3)?

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Q: Directions: Use the chain tule to comute the derivative y' and simplify your ansuer: 2. 1. %3D

A: Given, y=u2+u-2 ;             u=1x

Q: Activity 1: Find the derivative of y with respect to x. 1. у%3 3x -5 2. у%3D6 3. y = x2 + 4x 4. y =…

A: solve the following

Q: An inverted conical tank has height 5m and a diameter 10m. Water is draining from the tip of the…

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Q: compute th directional derivative of f(x,y) at point P in the direction of the point Q .

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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.