Find an equation of the tangent line to the graph of f at the given point. x + 2 1. -5 2. f(x) : X- 1

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

A: Here, y = g(x)  and g(3) = -5 i.e. when x1 = 3, then  y1 = -5 and g(3)=2 i.e. At x =3, the slope, m…

Q: C. If h(x) = [f(x)]² + g(x),what is the equation of the line tangent to the graph of h at x = -2?…

A: First we will find derivative of h(x) at x=(-2) that gives the slope of the required tangent.

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: 11. For the given function, find the value of x on the graph where the tangent line is horizontal. y…

A: Writing the equation in standard form.

Q: 7x Find the slope of the tangent line to the graph of f(x) = at x=2. (x+1)(x- 5)

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Q: For f(x) = 2x - 4x + 3 find the following. (A) f'(x) (B) The slope of the graph of f at x = - 4 (C)…

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Q: Find an equation of the curve whose tangent line has a slope of f'(x) = 4x 14/15 given that the…

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Q: Find an equation of the tangent line to the graph of y = g(x) at x = 6 if g(6) = -4 and g' (6) = 3.…

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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: g(x) : 15 — х2; (1, 14)

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Q: The graph of function f(x) is shown below. At which value of z is the slope of the tangent line to…

A: The given curve is a downward facing parabola as shown: Here, the highest point is at 3,-1. Thus,…

Q: 56. For what value of a does the graph of f (x) = e® – 2x have a horizontal tangent?

A: Given query is to find the value of x where tangent is horizontal.

Q: The slope of the tangent to the graph of f(x)=-Vx² - 1 at the point (-1, 0) is 1. a) man =0 b) man =…

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Q: Find an equation for the line tangent to the graph of 7x f(x) = x + 3 the point (2, 2.8).

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Q: 5. Find the slope of the tangent at the given points for the function S4 – x², x 15 а) P(- 1, 3) b)…

A: Topic- application of derivatives

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: Find an equation of the tangent line to the graph of y = g(x) at x = 6 if g(6) = -4 andg' (6) = 3.…

A: Slope intercept form-  Y = mx + c  m = slope = g'(x) At x=6,  m= g'(6) =3 c= intercept on y axis…

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: Q6. Find the equation of the tangent line to the graph f(x)=2xsinx at x=n

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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: 1. For the function f(x) = 2x? + 7x – 3, - (a). Find the slope of the tangent line at x = 2. [1Mark]…

A: The answers are : (a)  15  (b) y = 15x - 11   The detailed solution is as follows below:

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

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Q: 5x - 8 Find the equation of the tangent line to the graph of f(x) = x +1 at the point at which x =…

A: Equation of tangent line is (y-y1)=m(x-x1)

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 4 if g(4) = -2 and g'(4) = 3.…

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Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

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Q: Find the function whose tangent line has the slope e for each value of x and whose graph passes…

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Q: Let f(x) = 12 – x2 The slope of the tangent line to the graph of f(x) at - the point ( - 3, 3) is…

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Q: Find h'(-3) if h = f o g, f(x) = -8x? + 6 and the equation of the tangent line of g at -3 is y = 7x…

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Q: Consider the function and point given below. f(x) (-1, 10) х, х* (a) Find an equation of the tangent…

A: Consider the given function:

Q: Find an equation of the tangent line to the graph of y = g(x) at x = 2 if g(2) = -4 and g'(2) = 5.…

A: Given function is                                              y=g(x), at x=2g(2)=-4 and g'(2)=5 we…

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

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Q: Find an equation for the tangent line to the graph of the given function at (4,25). f(x) = x² + 9…

A: Given graph isf(x) = x2+9we have to find the equation of the tangent line at (4,25)we have f(x) =…

Q: Find f(3) if f"(x) = 2 and at the point (2, 6) the slope of the tangent line to f is 10.

A: we have to find f(3) if f"(x) = 2 and at the point (2, 6) the slope of the tangent line to f is 10.

Q: Find f(3) if f"(x) = 2 and at the point (2,6) the slope of the tangent line to f is 10

A: Given that: f''x=2 At the points the slope of tangent line to the function is 10 So, f'x=10

Q: 1. Find the slope of the tangent line to the graph of the following function at the indicated point,…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Find the equation of the tangent line to the graph of the function f (x) = a+3 at the point (0,-).…

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Q: 13 Let f(x) 13 is 4 The slope of the tangent line to the graph of f(x) at the point 4, 13 The…

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Q: 2x-5 Find the equation of the tangent line to the graph of f(x) = at the point at which x+1 x = 0.

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Q: Find the equation of the tangent line to the graph of f(x) at the (x, y)-coordinate indicated below.…

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Q: 1. Find the equation of the tangent line to the graph f(x) = 2x² + 5 at P(-1,7) 2. Find the equation…

A: The solution to given questions is explained below.

Q: Consider the following f(x)=1/2x In x^2, (-1,0) Find an equation of the tangent line to the graph…

A: Tangent  line to be find

Q: 1. For the function f(x) = 4x? + 6x – 6, (a) Find the slope of f(x) at x = 4 (b) Find equation of…

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Q: Find an equation of the tangent line to the graph of y = g(x) at x = 4 if g(4) = -6 and g'(4) = 3.…

A: The tangent line is a Straight line which is a tangent to the curve at the point. The point here…

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

A: 1)y=f(x)=x+2 y'=1 At (6,4), y-y1=m(x-x1) y-4=1(x-6) x-y-2=0 2) y=f(x)=x-2 y'=1 At (6,4),…

Q: 2. Write the equation of the tangent line to the curve y = x2 -x-2+ 2 at the point P(1, 2). 3. Use…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

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

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Q: Where on the curve of 1 does the tangent have the greatest positive slope? y = 1+ x? O 1) 3 3 O 2) 3…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: