Find the linear approximation of the function g(x) = 1+x at a = 0 and use it to approximate the numbers 0.95 and 1.1. Illustrate by graphing g and the tangent line.

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: find the equation of the tangent line at x=-6 for f(x)=x^3/2. write the answer in the form y=mx+b

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Q: .) Write the equation of the normal line of f(x)=2x^2-1/x at x=1? b.) Let y=4x^4+x. At what point…

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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: Find the equation of tangent line of the function f(r) = e"/x at the point a = 1. Write in the form…

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Q: Find the equation of the tangent line to the function f(x) = e*-1 In(x + 1) when x = 0.

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Q: Find a number a such that the tangent line to the graph v= 3x at x = a is parallel to the tangent…

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Q: Find the tangent line to g (x)

A: Given, g(x)=16x-4x

Q: Find f(4) and f'(4), assuming that the tangent line to y = f(x) at a = 4 is y = -7x +2.

A: The derivative of a function at a point represents the slopeof tangent at that point .

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: Compute f ' (x) and find an equation of the tangent line to the graph at x = a. f(x) = 3√x,  a= 8

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find an equation of the tangent line to the graph of the function at the given point , y = x2ex −…

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Q: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 5x²;…

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Q: Find the equation of the tangent line to f at x = a. f (x) = x2 + x, a = 1

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

A: Consider the equation

Q: Find the equation of the tangent line to the function f(x)=2x^2−9 at the point where x=−6. Give your…

A: Calculate the derivative of the function at given point than write the equation of tangent line.

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: 2. Given the function, find the slope of the line tangent to the curve: f(x) = v5x + 2 at the point…

A: We have to find the slope of the line tangent to the curve: f(x)=5x+2 at the point P(1,2) for the…

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

A: We have to find the equation of tangent line to the graph of function fx=esecx at the point π4, e2.…

Q: Find an equation of the tangent line to the graph of f at the given point. f(x) Vx, (81, 9) y =

A: Slope of the tangent is obtained by dy/dx

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: Compute f'(x) and find an equation of the tangent line to the graph at x = a. f (x) = 5x − 32√x, a =…

A: For a function f(x), f'(x) denotes its first derivative. Value of first derivative at a point gives…

Q: Find an equation for the line tangent to the graph of…

A: Given function is fx=-2xex To find: Th equation of tangent line at point a,fa for a=2 Solution:…

Q: find an equation of the tangent line to the graph of the function f defined by the equation at the…

A: The equation of tangent line passing through the point x1,y1 is y-y1=mx-x1, where m is slope. The…

Q: Let f(x) = (x - 12) / (2x + 6) Find an equation for the tangent line to the graph of f at x = 2 y =…

A: We find f'(x) first using quotient rule

Q: Consider the function f(x) = 1/x and show it on grap. Find the equation of the tangent line at x =3.

A: Given function is fx=1x. To graph the function and the find the equation of the tangent line at x=3.…

Q: The slope of the tangent line to the graph of f(x)%3D at a =-1 is: x2 - Select one: 1. a. O b. O c.0

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Q: Find the equation of the tangent line to f- at the point P (-3, 1) for f(x) = - 1- 2x Provide your…

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Q: Let f(x) = 3x^2 + x + 5. a) Find the equation of the tangent line at x = 10. b) For what value of x…

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Q: Find an equation for the line tangent to the graph of f(x) = 2xe %3D at the point (a, f(a)) for a =…

A: f(x) = 2xexslope of tangent will be calculated by differentiation function f(x) at given point.f(x)…

Q: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 3/2 x +…

A: Here the given function

Q: Find all values of x for which the tangent line of f(x) = V x2 + 18x + 96 is horizontal.

A: Given that, the tangent line horizontal. That is it is parallel to x axis. The equation of the…

Q: Find the equation(s) of the tangent line to the graph of f(x) = x² +1 passing the point (3, 1).

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Q: Consider the function f(x) = 1/3x3 + 3/2x2 - 4x. At which point(s) is the slope of the tangent line…

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Q: Determine the value(s) of x for which f(x) = 9x + 8 has a horizontal tangent line

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Q: Find f(x) if f(1) 7 1 and the tangent line at (x, f(x)) has slope f(x) =

A: We know that the slope of tangent at any point to the curve of a function is given by the derivative…

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: Find the slope of the tangent to Ax) = x²e* at the point (1, e). a) e b) 1 c) 3e d) 2 + e

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Q: Find the slope of the tangent line to the graph of the function at the given point.    f(t) = 3t −t2…

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Q: Find the slope and equation of the tangent line to f(r) = 3+3x at a 3 using the definition. %3D

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

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Q: Find the equation of the tangent line to f- at the point P (-3, 1) for f(x) = 3 1- 2x Provide your…

A: see below the answer and explanation

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: Let f(x) = 2x* + 3x° + 10. Find the equation of the line tangent line to the graph of Y point (1,…

A: Given  f(x) = 2X⁴ +3X³ +10 We need to find the equation of tangent of f(x) at the point (1,15)

Q: Find the equation of the tangent line to f(x)=4x+x^−1/2+1 at the point (4,35/2)

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Q: Find an equation for the line tangent to the graph of: f(x)= 2xex at the point (a,f(a)) for a=2.

A: Given curve Now, we find f'(x) We know that slope of tangent line to the curve y=f(x) at point x=a…

Q: Suppose the curve y=f(x) has a tangent line y=4x-5 at x=1. Consider the function g(x)=2f(x)+x+1.…

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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.