Find an equation of the tangent line to the graph of f at the point (2, f(2)). f(x) = xV x2 + 60 y = Use a graphing utility to graph the function and the tangent line in the same viewing window. See Example 4.

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

A: Given,f(x)= -2x +5 and the point (1-,7)

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A: Given that: Curve of f(x)

Q: Graph the function f(x) = coordinates are -2,0, and 1. 2a? and draw the tangent lines to the graph…

A: Sketch the function.

Q: Using the criterion of the first and second derivatives, find the graph of the function c) F(x) = x…

A: Topic = Functions

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: To Determine: Find the equation for the function f that has given derivative and whose graph is…

Q: Let f(x)= 4x2 + An equation of the line L tangent to the graph of f at the point ( ) is (fill in the…

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Q: Find the slope m and the equation of the tangent line to the graph of the function f at the point…

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Q: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 19 – x²;…

A: The given data is: gx=19-x2 To find the slope of the tangent line at the point 3,10.

Q: Find the point on the graph of the function that is closest to the given point. Function Point f(x)…

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Q: Find the point on the graph of the given function at which the slope of the tangent line is the…

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Q: Using the definition, find the derivative of the simplest quadratic function y=x2.

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Q: The translation of a radical function is shown below. y - Va translated to y - V+3-2 Which graph…

A: The translation is the moving of the curve horizontally or vertically by specified units. If the…

Q: Find all values of x such that the slope of the line tangent to the graph of f(x) is 0: f(x) = 3x* +…

A: Given : f(x)= 3x4 +4x3-36x2+6343

Q: A3) Find the equation of the line tangent to the graph of f(x) = 5x+7x ---.

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Q: Using the criterion of the first and second derivatives, find the graph of the function a) F(x) = x³…

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Q: Find an equation of the line that is tangent to the graph of f and parallel to the given line.…

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Q: 78. For what values of x does the graph of f (a) = x³ + 3x? + x + 3 have a horizontal tangent? %3D…

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Q: Find the point on the graph of the given function at which the slope of the tangent line is the…

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Q: Given that f(-5)=-5  and f'(-5)=-10 , find an equation for the tangent line to the graph y=f(x) of…

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Q: O Find the equation of the line tangent to the graph of f(x) = 7x + 3x? – 4x - 8 a %3D

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Q: 14. Use the curve sketching procedure to analyze the function. a. y-x'+x²-20x а. 1+x? b. y=- 1-x?

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Q: Find the slope of the secant line between x=−1 and x=2 on the graph of the function f(x)=x3−4x2+5x.…

A: The slope of the secant line between x = −1 and x = 2 on the graph of the function f(x) = x3 − 4x2 +…

Q: A3) Find the equation of the line tangent to the graph of f(x) = 5x3 + 8x² – 2x – 3 at x = -7.

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Q: Find an equation of the line that is tangent to the graph of f and parallel to the given line.

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Q: Find the derivative of the function. 7x - 9 f(x) = f'(x) = Need Help? Read It

A: The answer is given below:

Q: For what values of x does the graph of f(x) = x3 + 3x 2 + x + 3 have a horizontal tangent?

A: the given function is: fx=x3+3x2+x+3 we have to determine for what values of x does the graph of…

Q: Given f(x) = –3x² – x + 15, find f' (-3) using the definition of a derivative. Provide your answer…

A: f(x) = -3x2 -x +15 find f-1(-3)

Q: Find an equation of the line that is tangent to the graph of f and parallel to the given line.…

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Q: Solve the Problem. Approximate the curve of the given function f. f(x) = x³ + 2x2 – 15x

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Q: Write the equation of tangent line to the graph of y= x^2-9x/3x-x^3 at x= 3. Chex the reasonableness…

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Q: Find the point on the graph of the given function at which the slope of the tangent line is the…

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Q: Graph the function f(z) = – 2x´ and draw the tangent lines to the graph at points whose…

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Q: For what values of x does the graph of f(x) =x³ + 9x² +x + 5 have a horizontal tangent?

A: GIVEN : f(x) = x3 + 9x2 + x + 5

Q: Find an equation for the line tangent to the graph of the given function at the indicated point. x3…

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Q: Write the equation of the line tangent to the graph of f(x) = -3x² + 5x +1 at x=1 and use it to…

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Q: 3x² + 2x–1 Write the equation of the tangent line to f(x)= when x = - 1. x' - 4x+1

A: To find the equation of tangent line to the given curve at a given point, Obtain the expression for…

Q: Suppose f(5) - 9 and f'(5) = = - 3. - An object moves along the curve y³ - 3x² f(x) = 5x = 649. For…

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Q: Find the derivative of the function. (Simplify your answer completely.) f(x) = In(x7 - 7)7

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Q: Find the point P on the graph of the function y=√x closest to the point (5,0) The x coordinate of P…

A: Since, we have to find a point P on the graph of the function y=x -(i) closest to the point…

Q: Find the derivative of the function. (x) = (2x – 6)ª(x² + x + 1)5 %3D f'(x) = Need Help? Watch It

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Q: Determine an equation for the line tangent to the graph of the given function at the indicated point…

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Q: find the slope and an equation of the tangent line to the graph of the function f at the specified…

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Q: The graph f(x) has horizontal tangents when x = 3 f'(x) 2+ 2 -1 0

A: Horizontal tangents have slope = 0. ie slope of tangent = f'(x)

Q: Find the derivative of the function.

A: The given function is gx=3x2-22x+3-2.

Q: Find the function f given that the slope of the tangent line at any point (x, f(x)) is f'(x) and…

A: Integrate and pass that through given point for value of constant

Q: Use the four-step process to find the slope of the tangent line to the graph of the given function…

A: This is the definition of  derivative of a function.

Q: f(x) = 3x³ – 9x² + *+3 Determine the equation of a line parallel to the tangent to f(x) at x = 4.

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Q: Find the slope of the secant line between x = -2 and x = 3 on the graph of the function f(x) = -2x2…

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Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: f'x=-2x8-x2    passes through the point2,2x,y=2,2Indefinite integral:∫f'x dx=Fx+C

Q: Consider the function f(x) = x3 + 4, and the point (1, 5). Write the equation of the line tangent to…

A: Compute the slope as follows.

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: