f (x) X - 9 ) (smaller x-v (x, y) = ([ (x, y) = (C ) (larger x-va %3D

Q: Find an equation of the tangent line to the graph of the function f through the point (xo, Yo) not…

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Q: Determine the value(s) of x where the tangent to g(x) = (x + 5)(x2 - 1) is parallel to y = -7x - 8

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Q: an equation of the line tangent to the function of x2 + (y – x)2 = 9 at x = 1.

A: At given value of x find y Differentiate at given value Use equation of tangent line

Q: Find an equation of the tangent line to the graph of the equation at the given point : g(x) = x³ +…

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Q: Find an equation for the tangent line to the graph of the given function at ( – 5,32). - f(x)=x² +7…

A: Given query is to find equation of the tangent line.

Q: Find an equation of the tangent line to the graph of the function at the given point. y = (e4x −…

A: We first have to find y'We apply exponent rule and chain rule.y'= 8(e^(4x))*(e^(4x)) -4)

Q: x²+16x Let f(x) : = *+16x Find the value of x such that the tangent line to y = f(x) is horizontal.…

A: We know slope is given by derivative of f(x) w.r.t. x And tangent line is horizontal When slope is…

Q: 5) Prove that the function y = tan x has no horizontal tangent lines. Do NOT show me a graph as a…

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Q: Find the equation of the tangent line to the graph of ​f(x)=3/x at (9,1/3). The equation of the…

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Q: 6. If f(x) = 3x2 . - x find f'(x), then find the equation of tangent line at r = 5.

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

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Q: Find an equation of the curve whose tangent line has a slope of f'(x) = 3x 10/11 given that the…

A: Given is derivative of f(x) we find f(x) so we integrate it.

Q: The tangent line to the graph of y = g(x) at the point (4, 5) passes through the point (7, 0). Find…

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Q: :-1 What is the slope of the tangent line that touches the graph of In(y) +e-'=3y – 4x at the point…

A: As per guidelines we have to solve the 1st one

Q: 5) Find all points (x, y) on the graph of y = - with tangent lines perpendicular to the (x - 4) line…

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Q: a. Sketch the curve f(x) =x/(x-1)^2 b. Find the equation of the tangent line and normal line of the…

A: a) f(x)=x(x-1)2b) y3+3xy+x4=5 at the point (1,1)

Q: Find all points (x,y) on the graph of f(x) = 2x- 3x with tangent lines parallel to the line y= 13x +…

A: Given : f(x) = 2x2 - 3x     To find the points on the graph of f(x) = 2x2 - 3x with tangent lines…

Q: A) Find an equation of the line tangent to the function of x2 + (y- x)2 = 9 at x = 1. %3D

A: Given, The function  x2+y-x2 = 9  We have to find the equation of the tangent line to function at x…

Q: The graph of ax + b f(x) = (x+ 1)² has a horizontal tangent line at (-2, –1). Find a and b.

A: Given,           The graph of fx=ax+bx+12 has a horizontal tangent line at -2,-1.

Q: Find an equation of the tangent line to the graph of f(x) =2- 5x at (2, – 18). The equation of the…

A: A function is a relation which maps each value in its domain to exactly one value in its range.…

Q: 10. Find an equation of the tangent line to the graph of y = x - 3x? + 2 at (1,0). 11. Find an…

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Q: Find all points (x, y) on the graph of f(x) = x? with tangent lines passing through the point (3,…

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Q: 11. Algebraically find the x-coordinate of all points where the given function has a horizontal…

A: Given: y=2x3+3x2-36x+1, y=2x+13x-2 We know that if any curvey=fx have horizontal tangent then slopem…

Q: Let f(4) = -5 and f'(4) = 6. Then the equation of the tangent line to the graph of y = f (x) at x =…

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Q: Find the equation of the line tangent to the graph of f(x)=4cos(x) at x=−π/3 Give your answer in…

A: Given :f(x) = 4cosx at x = -π3We will find the equation of tangent line

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 4 if g(4) = -3 and g'(4) = 5.…

A: y=g(x) and g(4)=-3 , g'(4)=5 we have to find the tangent line of the given function y=f(x)

Q: х — 7 - f(x) = %3D 5х + 7 Find an equation for the tangent line to the graph of f at x = 3.

A: Given: fx=x-75x+7 To find the tangent line, we find the slope Therefore differentiate with respect…

Q: 49. Find an equation of the tangent line to the graph of y = 8/(x² + 4) at (a) (0, 2); (b) (–2, 1).

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Q: Richa< decline under question out of Scope> Find the equation of the tangent line to…

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Q: 4- x Find the equation of the tangent line tof-l at the point P (G, 1) for f(x) = x+1 Provide your…

A: Topic:- application of derivatives

Q: What is the slope of the tangent line to the graph of y= x*-3x2 + x +2 at x-17 [a) What is the…

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Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = In x°;…

A: Solution: The objective is to find the equation of the line

Q: Find h'(-3) if h = f o g, f(x) = 8x? – 2 and the equation of the tangent line of g at -3 is y = -3x…

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Q: The tangent line to the graph of y = g(x) at the point (6, 4) passes through the point (2, 9). Find…

A: The tangent line to the graph y=g(x) at the point (6,4) passes through the point (2,9). Note:…

Q: 3. A function is defined by the equation y = V3x + 4, where does the slope of the tangent line equal…

A: Given,           A function is defined by the equation y=3x+4 and the slope of the tangent line…

Q: The tangent line to the graph of y = g(x) at the point (9, 1) passes through the point (4, 6). Find…

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Q: Find an equation of the tangent line to the graph of f at the point (2, f(2)). f(x) = xVx2 + 60 y =

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Q: f(x+h)- f(x) 4x3+9x+5 Using lim0 Find the slope of the tangent line y = Зx-8 h at x = -1.

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Q: Find an equation of the tangent line to the graph of y = g(x) at x = 3 if g(3) = -2 and g'(3) = 5.…

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Q: (c) Find the slope of the tangent to the graph of y = f(x) at x = -1. (d) Find the point on the…

A: Slope of tangent = dy/dx

Q: Consider the function f(x) = 9x² +3. Its tangent line at x = 6 goes through the points (1, y1) and…

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Q: 1 and y = g(æ) has a 1, then the graph of y = f(x)g(x) has a horizontal tangent line at ) and g(x)…

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Q: Find the equation of the line tangent to the graph of f(x) = −3cos(x) at x = −π/3   Give your…

A: First, find the point of tang-ency. We know the x value we now have to find y value  Substitute in…

Q: Solve the problem. Find where all tangents to the curve f(x) = that have slope -1. x + O x = 0 O x =…

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Q: 5 Let f(x) = 2+ - (a) Find f' (x). f' (x) = (b) Find the slope of the tangent line at x = 5. Slope =…

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Q: 13. BONUS: Find the coordinates of all points on the graph of y=1-x at which the tangent line passes…

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Q: The straight line y=x +B is tangent to the graph of f(x) = 2^{x at the point where x = A. Find A and…

A: The staright line y=13x+B is tangent to the graph of f(x)=2x at the point where x = A, we have to…

Q: Find an equation of the tangent line to the graph of y=g(x) at x=5 if g(x)=-6 and g’(5)=2. Answer…

A: We have to find equation of tangent line

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.