Consider the following. f(x) = x In xº, (-1, 0) (a) Find an equation of the tangent line to the graph of the function at the indicated point. (Use x for the independent variable and y for the dependent variable.) (b) Use a graphing utility to graph the function and its tangent line at the point.

Q: 2. Determine an equation for the tangent line to f(x) = x(x² + 1)3 at x = -1.

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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: Find an equation of the tangent line to the graph of the function at the given point.

A: Given, f(x)=e3x, 0,1 We need to find an equation of the tangent line to the graph of the function at…

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: Find the equation of the line that is tangent to the graph of the function f(x) = ln(8x + 6) at the…

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Q: 2. Find the equation of the tangent line to the graph of the function at the indicated point. (a)…

A: Explanation of the answer is as follows

Q: Find the slope-intercept equation of the tangent line to the graph of f(x) =√x at (1, 1).

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Q: Using the definition of the derivative, find f'(x) for the following function. 4. f(x) = - x² + 8x -…

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Q: Find the equation of the tangent line to the graph of the function f (x) = (x² + 8) (x – 3) at the…

A: The gradient of the tangent at any particular point is given by :     f(x) = (x2 + 8) (x - 3)…

Q: 2 Find the equation of the tangent line to the graph of f(x) = at The equation of the tangent line…

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Q: 2) Find the equation of the tangent line to the graph of x? + (y – x)3 = 9 at the point x = 1.

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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: 1. Consider the function f (x) = 2(3x³ – 2x²)5. %3D a. Differentiate the function. b. Find the slope…

A: 1) Given: the function fx=23x3-2x25.

Q: 14. Find the equation of the line tangent to the graph of f(x) = 2x3-x + 1 at x = -1. %3D

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Q: 3b. Find an equation of the tangent line to f(x)=2x+x-1 at the point Where x 1. %3D

A: The solution of the problem is given in the next step.

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A: The given function is f(x)=x+1x-6at the point 0,-16 To find the equation of the tangent line the…

Q: Find an equation of the tangent line to the graph of the function at the given point.

A: Our Aim is to find an equation of the tangent line to the graph of the function f(x)=e-x-6-(i) at…

Q: How do you solve question 9?

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Q: Find the equation of the tangent line to the graph of the function f(x) = v2x² + 1 at the point…

A: Given that: f(x)=2x2+1        at point (2, 3)

Q: f (x) = x² + Vx at the point x = 1

A: Consider the given: fx=x2+xf1=12+1f1=1+1f1=2Find the derivative:f'x=2x+12xAt…

Q: 2. Find the slope of the tangent line to the curve f (x) = -1 2 at x

A: Given: f(x)=2x

Q: Find the equation of the tangent line to f(x) = x² + x at x = 3. Sketch the function and this…

A: The slope of any curve at any point is equal to the derivative of the curve at that point. The…

Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = el-x,…

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Q: Find the equation of the tangent line to the graph of the function f(x) = x² +x – 1 at the point…

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Q: II. Find an equation of the tangent line to the curve of f(x) =-2x' +6x+1 when x 23

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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: Given f (x) = x³ + x² + x + 1 and its derivative f'(x) = 3x² + 2x + 1, find the equation of 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: Find the equation of the tangent line to the graph of the function f(x)=(x+3)/(x−4) at the point…

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Q: Find an equation of the tangent line to the graph of the function at the given point. y = 2−x, (−1,…

A: Given: y=2-x  ,-1,2

Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) =  3x…

A: Point of tangency = (2, 8)m = slope of the tangent line = f'(x) at the point of tangency =…

Q: Find the equation of the tangent line to f(x) = (x^2) − 4x + 1 at (x=3).

A: We first find f'(3) So the slope is 2

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: Find an equation of the tangent line to the graph of the given function at the specified point. x² –…

A: We have to find the equation of the tangent line

Q: Determine the equation of the tangent line to the function g(x) = (2ex)/x at the point, (2, e2).

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Q: Find the equation of Tangent line to the graph of f-1 at the indicated point p(2, 1) of the…

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Q: 8. For the function f(x) = x2 - 2, find: a) The slope of a tangent line at x = a.

A: To find the slope of tangent line at x=a.

Q: 12. (a) Use the definition of derivative to find the slope of the tangent line to the curve f(x) =…

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Q: Find an equation of the tangent line to the graph of ​f(x)=ex​, where x=−0.3.   The equation of the…

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Q: 1. For the function f(x) = 3x² + 8x – 7, (a) Find the slope of f(x) at x = 3 (b) Find equation of…

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Q: 2. Find the equation of the tangent line to the graph of f(x) = 3x?e-1 - 1, at r = 1.

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Q: Find an equation of the tangent line to the graph of the function at the given point.   f(x) =…

A: Given,     f(x) = ln(9(x+4)/x); (-9/2,0) Let m be the slope of required tangent line.

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

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Q: 12. Find the equation of the tangent line to the given function at the point (0,1). f(x) = In(3xe¬x)

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Q: Find the values of x where the tangent line is horizontal for the function  f(x) = x2(x-5)3

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Q: 12. Find the equation of the tangent line to f (x) = x³ at the point P(1,1).

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Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = e-X…

A: Given: f(x)=e-xln(x)

Q: Find the equation of the tangent line to the graph of the function f(x)=(x2+8)(x−3) at the point…

A: Given: y=fx=x2+8x-3 at 0,-24 we know that for finding equation of tangent we need to find slopem of…

Q: Find an equation of the tangent line to the graph of f(x) = 2 + e1−x at the point (1, 3).

A: We have to find equation of tangent line to the graph of function fx=2+e1-x at the point 1, 3. We…

Q: Find an equation of the tangent line to the graph of the function h(x) = −xe2−x, at the given point…

A: Slope of the tangent line is the derivative of the given curve at the given point. So…