Estimate the instantaneous rate of change of y(t) = 2t- 6 at the point: t = - 3 In other words, choose x-values that are getting closer and closer to -3 and compute the slope of the secant lines at each value. Then, use the trend/pattern you see to estimate the slope of the tangent line. Your answer should be accurate to at least 2 decimal places.

Q: (a) Find the slope of the tangent line to the function y 3+sec (x) at 1-sec (x) X = -. 4

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

Q: Find the equation of the tangent and normal line to the curve y=x2 at x=1

A: Tangent is a line to the curve that just touches the curve at a particular point. Normal is a line…

Q: Let f(x) = x² – 4x + 4. (a) Find the derivative of f. (b) Find the point on the graph of f where the…

A: Given function is f(x)=x2-4x+4 then a) derivative of function is f'(x)=2x-4 Derivative of the…

Q: Find the slope of the tangent to the curve at the point specified. x² +y² = 9 at (0, 3) The slope is

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Q: For the function  y = (x2 + 2)(x3 − 9x),  at  (−3, 0)  find the following. (a) the slope of the…

A: (a) To find: The slope of the tangent line at -3,0. Given: The function is y=x2+2x3-9x. Concept…

Q: Find an equation of the form y = f(x) for a curve with æ-intercept 0 whose tangent line at any point…

A: We have to find

Q: Estimate the instantaneous rate of change of y(t)=4t^2+5 at the point: t=−1 In other words, choose…

A: Given: y(t)=4t2+5. Now,          y'(t)=8t. At t = -1,           y'(-1)=8(-1)=-8.

Q: (b) y = x3 y 2 1

A: Given y=x³ Draw the graph and measure the change in y and change in x

Q: Use the graph to estimate the slope of the tangent line to y = xn at the point (1, 1). Verify your…

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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: 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: Estimate the slope of the tangent line at the point t= -2 for f(t) = 6t-3 (Give answer as a…

A: The given function is f(t)=6t-3 at t=-2

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: Find an equation of the tangent line to the curve at the following point:  y=4/1+e^-x, (0,2) y=?

A: We first find the slope of the tangent using the first derivative y=41+e-xy=4(1+e-x)-1…

Q: Estimate the slope of the tangent line at the point t = -7, for f(t) = 15t – 1. (Give your answer as…

A: Slope of tangent line

Q: The tangent lines to the graph of f(x) = x2 grow steeper as x increases. At what rate do the slopes…

A: The tangent line of any given function is the line which  touches the curve of function at only one…

Q: Use the graph to estimate the slope of the tangent line to y = xn at the point (1, 1). Verify your…

A: Use the graph to estimate the slope of the tangent line to y = xn at the point (1, 1). and to verify…

Q: Find the equation of the tangent line and normal line to the given curve at the specified point. y =…

A: The given equation is,

Q: Let f(x) = 6 - 3x + 5x2. (a) Find f'(a) (b) What is the instantaneous rate of change of f when x =…

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Q: 4) Estimate the instantaneous rate of change of function f(x) = x + 5x' +2 at x = -3 b) Determine…

A: Given that fx=x4+5x3+2First, we will find the instantaneous rate of change of the functionat x=-3.

Q: Find the equation of the tangent line to the curve y = 4 ln at the point (1, 4). (Hint: simplify…

A: Curve given is- y=4ln(x3ex3) We need to find the equation of the tangent line to the curve at the…

Q: (a) Determine the slope of curve y = x · Ln(x) at x = 3.

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

Q: If the instantaneous rate of change of g(x) at (-1, -2) is 1/2, write the equation of the line…

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Q: If the instantaneous rate of change of g(x) at (−1, −3) is 1/2, write the equation of the line…

A: Slope of tangent line is ½. So the equation is of the form:

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: Find all points on the curve  x 2  y 2 + xy = 2  where the slope of the tangent line is - 1

A: We first find dy/dx using implicit differentiation

Q: Find the points on the graph of y = ex + e-2x where the tangent line is horizontal.

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Q: Suppose x and y are functions of third variable t. In the equation *+y=45, what are the values of…

A: First we will find value of y from given equation And differentiate wrt to t

Q: If the instantaneous rate of change of f(x) at (4, −3) is 7, write the equation of the line tangent…

A: The objective is to find the equation of the tangent line to the graph of f(x) at x=4.

Q: A ball is thrown straight up with an initial velocity of 112 ft/sec, so that its height (in feet)…

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Q: Use the graph to estimate the slope of the tangent line to y = xn at the point (1, 1). Verify your…

A: Given curve is y=x-1. Power rule of differentiation states that, ddxxn=nxn-1 Differentiating the…

Q: For the function y= x^2+5/x+5 at (1,1), find the following. ( give exact answer. Do not round ) (A)…

A: Given: y=x2+5x+5 ; Px,y=1,1 (A). As we know that, the slope of the tangent line to the curve at a…

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: II FIND THE EQUATION OF THE TANGENT LINE AND NORMAL LINE TO THE FF. CURVES AT THE INDICATED POINT.

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Q: Use the graph to estimate the slope of the tangent line to y = xn at the point (1, 1). Verify your…

A: Estimate the slope of the tangent line to y=x12 at the point (1, 1) and then verify the answer…

Q: Differentiate implicitly to find the slope of the curve at the given point. 2) x2 + y2 = 1; (2, 3)…

A: We will solve the following.

Q: Consider the function Y3x2-6×+ス a. Find the slope of the tangent lihe to the curve at x=2 be Find…

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Q: Find the slope of the line tangent to the curve y = sin x at the point where x = 3

A: Given: y=sin5x To find: The slope of the line tangent to the curve y=sin5x at the point where x=π3

Q: Find an equation of the tangent line to the curve, x^2-xy-y^2=1 at the point (2,1). (use implicit…

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Q: Q-2- Find the eAuation of the tangent line.and the normal line for the fallowing function X = 0-…

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Q: For the function  y = (x2 + 3)(x3 − 9x),  at  (−3, 0)  find the following. (a) the slope of the…

A: Given Data: Function: y = (x2 + 3)(x3 − 9x) Point: (x, y)=(-3, 0) (a) The derivative of the given…

Q: For the function y = (x2 + 4)(x - 4x), at (-2, 0) find the following. (a) the slope of the tangent…

A: Solution:-

Q: The tangent lines to the graph of f (x) = x2 grow steeper as x increases. At what rate do the slopes…

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Q: Find the equation of tangent and equation of normal for the implicit function y² +4xy = x+y, at the…

A: We have to find the equation of the tangent and equation of the normal for the implicit function y2…

Q: Find the slope of the tangent line to the curve x+y3D6 xy at the point (3,3). (a) 0 (b) -1 (c) 1 (d)…

A: To find: slope of tangent line at the point (3,3) to the equation of curve given below.

Q: The slope of the tangent line to the curve y=2e10xcos(-6x) at x-0 is

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Q: Estimate the instantaneous rate of change of P(t) = 5t + 6 at the point: t = 3 In other words,…

A: Given that Pt=5t2+6 To find the instantaneous rate of change of P(t) at point t=3.

Q: For the function y = (x2 + 2)(x3 - 9x), at (-3,0) find the following. (a) the slope of the tangent…

A: The given function is y=x2+2x3-9x. Differentiate fx with respect to x.…

Q: Find the equation of the line tangent to the graph of y = 3e" at r = 4. Tangent Line: y

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Q: Find the x-coordinate of the point on the graph of y=x^2 where the tangent line is parallel to the…

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