Pulling up to a traffic light, a car's velocity (in yards per second) follows the function f (t) = 16 – t as it - begins to slow down. Find the approximate distance the car travels from t = 0 to t = 5 using a left hand estimate with rectangles of width 1. а. 81 yards b. 80 yards О с. 92 yards d. 70 yards е. 63 yards

Q: The slope of the tangent line to the graph of the function y = 2/x – 6 at (36, 6) is 6 -0.50 0.17…

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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: Daily crude oil production by one particular oil company for 2008-2013 could be approximated by P (…

A: The given function is Pt=0.009t2-0.7t+3.43. Compute the average rate of change of P ( t ) over the…

Q: 1. FIND THE SLOPE OF THE TANGENT LINE TO THE GRAPH OF THE FUNCTION f(x) = 5 – x² AT (3,–4).

A: f(x)=5-x2 To find the slope of tangent, we can use two alternatives (1) Direct derivative (2)…

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: 9) Find the equation of the tangent line to the function f(x)=-3x² - 2x at the point where x=1. Give…

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Q: 3) Find an equation for the tangent line to the graph at the specified value of x. y=x²V5-x² ,x=1

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Q: Suppose that a company can produce 12,000 units when the number of hours of skilled labor y and…

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Q: Suppose f(3) = 6 and f '(3) = 7. Find an equation of the tangent line to H(x) at x=3. %3D H(x) =…

A: We have,  Hx=x4-7fx, f3=6 and f'3=7 Using the chain rule of differentiation, H'x=x4-7·f'x+fx·4x3…

Q: Find the equation of the tangent line to the function f(x)=−2x^3−3x^2−2x at the point (−1,1). Give…

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Q: 2. Determine the equation of the line perpendicular to the tangent line to the function f(x) = e' at…

A: We will find the equation of the line.

Q: 4. Find an equation of the line tangent to g(x) = 3x² - x +1 at x= 1.

A: Given function

Q: 34. Find an equation of the line tangent to the graph of f(x) = (2x – 1)(x + 4) at (1, 5).

A: The objective of the question is find the equation of tangent at the point (1,5).

Q: A factory can produce R rugs a month based on the function R(n) 4n2 – 7n +58, where n is the number…

A: Consider the given function of number of rugs: Rn=4n2-7n+58 Where, nx=15x+20x Rate change in rugs is…

Q: 22. Find an equation of the tangent line to the graph of f(x) = 4 - x² at (a) (-1,3); (b) (0, 4);…

A: Given: f(x)=4-x2 To Find: the equation of the tangent line to the graph at a) (-1, 3) b) (0, 4)…

Q: Lemons are harvested from a certain orchard at a rate modeled by L(t)= 20t - t^2 bushels per hour…

A: The rate is given by the function L(t) = 20t -t2, and the values of t vary between 0 to 10. The…

Q: For the functiony = 8x2 + 6x + 5,at the pointx = 8,find the following.(a) the slope of the tangent…

A: Given a function y = 8x2+6x+5.For any funtion f(x) the slope of the tangent at point x=a is…

Q: 1. Find the slope of the line tangent to the graph of f (x) = x³ In (x² – 5x + 7) at x = 2. - Do NOT…

A: We have to find slope to given equation by derivative.

Q: A company finds that the rate at which the quantity of a product that consumers demand changes with…

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Q: Find the equation of the tangent line to the graph of the function f(z) = V6z4 + 10 at the point (1,…

A: Given: fx=6x4+10 To Find: Find the equation of the tangent line to the graph of the function fx at…

Q: 1. FIND THE SLOPE OF THE TANGENT LINE TO THE GRAPH OF THE FUNCTION f(x) = x2 + x - 1 AT (-2, 1). %3D

A: As per our guidelines, we are providing the solution of question number 1 only. Please repost the…

Q: 25.For which x – values does the graph of y = e3x³-2x-4x have a horizontal tangent line ?

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Q: The slope of the tangent line to the graph of the function y = 9/x – 7 at (49, 56) is . O -1.14 O…

A: Given,  The function  y = 9x - 7   We have to find the slope of the tangent line at 49, 56.

Q: For the function f(x) = x² – 4 at the point (4, 12), find: a. the slope of the curve using the…

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Q: 19 Find all x-values where the tangent line is horizontal for the function v(x) = x3 − 12x + 10

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Q: 4. Find the slope of the tangent line to the function f(x)= +3; x+2 at x = 4 5x-10

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Q: (4) Find the equation of the line tangent to f(x) = 12√ - 2² at the point (4,8).

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Q: 1) Find the slope of the tangent line to the graph of f(x) = x2 - 3 at the point (2, 1). %3D (8…

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Q: 4) Determine the equation of the tangent line to the function 2 f(x) = x at the point (3, 9).

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Q: For the function  y =  x2 + 4 x + 16   at  (4, 1),  find the following. (Give exact answers. Do…

A: The instantaneous rate of change is the change in the rate at a particular instant, and it is same…

Q: 7. Determine the equation of the tangent to the function E-2 f(x)=- at x= 1.

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Q: The slope of the tangent line to the graph of the function y= 8/T-6 at (36, 42) is O -1.50 6 O 0.67…

A: Slove of the tangent to the function y at point (a,b) is m= y'(a).

Q: 7. Find the equation of a line tangent to the graph of f (x) = cotx at x = T/4. Show all steps

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Q: find the slope of the curve x = e^-tcost2t, y=e^-2tsin2t at the point t= 0

A: find out the slope of the curve at t=0

Q: If a ball is thrown into the air with a velocity of 80ft/s, its height in feet after t seconds if…

A: Given y=80t-16t2 ; V=80 ft/SDifferentiate w.r.t 't'dydx=801-162tdydt=80-32tWe know that ,At…

Q: 4. Find the tangent line to the function f(x) =;xVx² + 5 at the point (2,2).

A: Tangent line of a function:  Differentiate the equation of the curve Substitute the value into the…

Q: 1. For the function f(x) = 4x² + 7x – 2, - (a). Find the slope of the tangent line at x = 4. (b).…

A: Given f(x)=4x²+7x-2 (a) to find the slope of tangent line at x=4 (b) to find the equation of tangent…

Q: The amount of insulin in microunits per mL in a diabetic patient is given by the function I(t) = 4.5…

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Q: 8) Find the equation of the line tangent to the graph of f(x) = x – :- at the point where x = 1.

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Q: Find f(x) if f(2) = 3 and the tangent line at x has slope (x - 1)e - 2x, - 2x 3 fx) 2

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Q: 6. Train E travels west toward Chicago station at 120 miles per hour while a second train N travels…

A: Train E =120 miles per hour  Train N=90 miles per hour

Q: The data entry speed (in entries per minute) of a data clerk trainee is represented by S = 10/0.6x +…

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Q: Suppose that f(x) = 3x² – 3. (A) Find the slope of the line tangent to f(x) at x = 5. (B) Find the…

A: We find f'(x) using the power rule Slope of the line tangent to f(x) at x=5 is given by f'(5) So to…

Q: The slope of the tangent line to the graph of the function y = 5/T – 4 at (16, 16) is , O -1.50 O…

A: We have to find the slope

Q: Suppose that f(x) = 5x² – 4. (A) Find the slope of the line tangent to f(x) at x = 5. (B Find the…

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Q: In Exercises 13–16, differentiate the functions and find the slope of the tangent line at the given…

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Q: 4. Find the equation of the tangent line to the function y = In (x² – 2) when x=3.

A: Question is solved.

Q: The slope of the tangent line to the graph of the function y = 8/T- 4 at (16, 28) is O 4 O -1.75 O…

A: Slope : It is the Differentiation of y with respect to x at a given point.

Q: The cost of producing a double filter respirator full face masks is c(x) = 15+ 10x a² (in dollars).…

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Q: Consider an isosceles triangle of base 16 inches and edges z, and assume that z is a function of…

A: Base of triangle = 16in  Edges = z in