by a(t) =5–2t m/ s² and its initial velocity (at 0 seconds) is v, =6 m/ s . · Find the velocity as a function of timc. . Find the displacement of the object on the interval from 0 seconds to 6 seconds. Find the average velocity on the interval from 0 seconds to 6 seconds.

Q: If the position function of a moving object is S(t) =t - 3t + 2 meters from zero in t seconds, then…

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Q: Estimate the slope of the tangent line of the function f(x) = 2e* at the point x = e. %3=

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Q: Find the equation of the tangent line to the curve f(x) = a² + 2x at x = 1. Enter the answer in the…

A: f(x) = x2 + 2x      at x=1  y = x2 + 2x   At x=1  =>  y = 12 + 2(1) = 1 + 2 = 3 point on the…

Q: If the instantaneous rate of change of f(x) at (8, −7) is 9, write the equation of the line tangent…

A: It's given that the instantaneous rate of change  of  f(x) at  (8,-7) is 9 . We have to find the…

Q: Find the derivative of the function. 8y9 y= In V+9 6.

A: The solution are next step

Q: Find the equation of the tangent line to the graph of the function f (x) = V 4x4 +12 at the point…

A: Given: The equation of a function is, f(x)=4x4+12. The objective is to find the equation of…

Q: For which value(s) of x does f(x)=−x^3/3−2x^2+3x−8 have a tangent line of slope 7?

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Q: find the derivative of V(t)=260e^(0.6298t

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Q: For the function y = 5x2 + 4x + 2, at the point x = 5, find the following. (a) the slope of the…

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Q: Q1. Write down the linear (tangent line) approximation to y = e x / 2 at the point x = 0, and…

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Q: Find the equation for the line tangent to g(x) rcos(x) at x = 0

A: Given:The function g(x) = (x cos(x))/(x+2).Obtain the tangent line for the above function at x = 0.

Q: For f(x)=x5, the instantaneous rate of change is known to be 405 at x=-3. Find the equation of the…

A: y=fx=x5instantaneous have of change is known to be 405 ,or x = -3∴ y=f-3=-35=-243

Q: Find an equation of the line tangent to f(x) = xcos x at x=-4. (Round coefficients to 3 decimal…

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Q: For f(x)=x5​, the instantaneous rate of change is known to be 5 at x=−1. Find the equation of the…

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Q: For the function P(x) = x3 − 7x, at the point (2, −6), find the following. (a) the slope of the…

A: Instantaneous rate of change of function is slope of tangent at any specific point

Q: If the instantaneous rate of change of f(x) at (4, −9) is 8, write the equation of the line tangent…

A: From the given statement, the rate of change of f(x) at (4, –9) is 8.That is,  f′(x) = 8.

Q: For the function y = 8x2 + 6x + 2, at the point x = 5, find the following. (a) the slope of the…

A: Given function is: y=8x2+6x+2 and the given point is x=5

Q: Find an equation of the line tangent to f(x) at the point |3D 1+e

A: Find slope at given point and then use formula  to find tangent line

Q: Find the derivative of the function w(s) = 10eVs.

A: To find the derivative of the below function. ws=10es

Q: Find the derivative of the function. z = (4 – t)(1 + t?) `

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Q: For the functiony =x2 + 3x + 9at(3, 1),find the following. (Give exact answers. Do not round.)(a)…

A: Given function y = x2+3x+9.The slope of the tangent line at a point(x,y)  is nothing but the value…

Q: If the instantaneous rate of change of fx) at (9, -6) is 2, write the equation of the line tangent…

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Q: For the function P(x) = x3 – 8x, at the point (3, 3), find the following. (a) the slope of the…

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Q: For the function y = 6x² + 5x + 6, at the point x = 7, find the following. %3D (a) the slope of the…

A: a) To find the slope of the tangent at x=7, we need dy/dx at x=7

Q: Find the slope of the line tangent to the given curve at the indicated point. a. f (x) = 3x + 10 at…

A: Given function,f(x)=3x+10,Aim:- To find the slope of the tangent of the curve f(x) at (-3,1)Let…

Q: Find f (3) and f' (3), assuming that the tangent line to y = f (x) at a = 3 has equation y = 5x + 2.

A: Tangent to a function at a point is a line which just touches the graph of the function at that…

Q: Compute f 1 (x) and find an equation of the tangent line to the graph at x = a. f (x) = x4 , a = 2

A: Consider the given function fx=x4  When x=2, then y=fx=24=16 Hence, point on the curve is 2, 16   To…

Q: 3. For the fiunction g(x) = x - 2x² –1, at what tangent point(s) is the instantaneous rate of change…

A: given function :

Q: For the function y = 2x2 + 8x + 9, at the point x = 6, find the following. (a) the slope of the…

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Q: Find an equation of the tangent line at x and f'(3) = 2. 3, assuming that f(3) = 5

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Q: Find the average rate of heating over the first 6 minutes. þÞ By drawing a tangent to the curve,…

A: Given graph represents the temperature (T° Celsius) of a metal ingot as it is heated over a period…

Q: 8. Find the equation of the tangent line to the curve y = e* at the point (a, f (a)) when a = In 3.

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Q: Find f(3) and f'(3), assuming that the tangent line to y = f(x) at a = 3 has equation y = 5x +2.

A: Consider the provided function, y=5x+2 Find the value of f3  and  f'3 at a=3. y=5x+2 We can write…

Q: For the function P(x) = x³ - 7x, at the point (2, -6), find the following. (a) the slope of the…

A: Note: The instantaneous rate of change is the slope of the tangent line at a point.

Q: 2) Find the equation of the tangent to f(z) = 3re² when x = 1

A: A detailed solution is given below.

Q: Find an equation of the tangent line to the function y 3x2 at the point P(1, 3). = Soluti

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Q: Find an equation for the line tangent to the graph of f at (1, 14), where f is given by f(x) = 30 -…

A: Please refer the attached image for complete solution.

Q: For the function y = 2x2 + 7x + 9, at the point x = 7, find the following. (a) the slope of the…

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Q: If the instantaneous rate of change of f(x) at (9, -7) is 6, write the equation of the line tangent…

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Q: For the function y 6x + 4x + 6, at the point x = 4, find the following. %D (a) the slope of the…

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Q: Find an equation of the tangent line to the function y = 3x at the point P(1, 3).

A: Given: The function y=3x2 . The equation of tangent line at the point Px1, y1 to the a curve y=fx…

Q: Assume f (x) = −4 / x. Find the equation of the line tangent to f (x) at (4, −1).

A: The given function is fx=-4x. To find the equation of line tangent at 4 ,-1. Solution: The given…

Q: Suppose the position function for a free-falling object on a certain planet is given by s(t) = - 131…

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Q: For the function  y = 6x2 + 5x + 1,  at the point  x = 5,  find the following. (a) the slope of…

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Q: If the minute hand of a clock has length r (in centimeters), find the rate at which it sweeps out…

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Q: If the instantaneous rate of change of f(x) at (6, −8) is 4, write the equation of the line tangent…

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Q: Find an equation of the tangent line to the curve at the given point. y = v x, (81, 9) y = |0

A: y = xdifferentiate with respect to x,dydx= 12xdydx(81,9)= 1281=118

Q: B) Find the slope of the line tangent to the curve y = sin3x at the point where x =

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Q: The slope of the tangent line to the graph of the function y = 4/T-6 at (36, 18) is | 0 36.00 O0.33…

A: slope is the first derivative of the function with respect to x.