Find the coordinates of points where the graph of f(x) = -x³ + 6x2 – 9x + 8 has horizontal tangents. As a check, graph f(x) and see whether the points you found look as though they have horizontal tangents. (x, y) = ( (smaller x-value) (x, y) = ( (larger x-value)

Q: Find f(x)=x-8/6x-1 and find the equation of the line tangent to the graph of f at x=2. and what is…

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Q: Find the slope of the secant line between x = 3 and x 5 on the graph of the function f(x) = -2x2 +…

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Q: f(x) = −x2 + 6x − 12 y-intercept(x, y)=

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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.…

A: Given function f(x)=2x2 and line is 6x-y+1=0

Q: a) Find the points on the graph of f(x) = 2x- 3r²- 12x + 8 where the tangent is 3. horizontal.

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Q: Find the relative maximum point of the curve: Y=16x+4x2-x4

A: Solution of question as follows

Q: Q5: (A): Finding a curve whose slope at the point (x, y)is 3x² if the curve is required to pass…

A: if the curve is passing through the point (1,-1) then we have to find the curve if the slope of the…

Q: Express f(x)= x2 +4x + 1 in standard form. Find thevertex of the graph and the maximum or minimum…

A: We will complete the square for f(x) Answer(a): Standard form: f(x)= (x+2)2 -3

Q: b) Find the slope of the function f(x) = VI+1at point (15,4).

A: The slope of  f(x) at a point (a,b) or x=a and f(a)=b is given by, df(x)dxx=a or f'(a)

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Q: Find the points on the graph for the function at the value f(x) = 3. x2 7x + 12

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Q: Find the point at which the line f(x) = - 2x +4 intersects the line g(a) = -a

A: Given, f(x)=-2x+4 and g(x)=-x

Q: Find the equation of the line that is tanget to f(x)= 1/x at the point (2,1/2).

A: We need to find the equation of the line that is tangent to f(x) = 1/x at the point (2,1/2).

Q: Find the slope of the secant line connecting the points on the graph f(x)=2h+4x-12, with the given…

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Q: Sketch the graph of the curve f(x)=3x³ - 3x + 2

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Q: The slope of the line tangent to the graph of f(x) = 12 – 2x? at the point x = -9 4 9.

A: Solution

Q: Use the Leading Coefficient Test to determine the end behavior of the graph of f(x) = x* – 4x?.

A: To Determine: use the leading coefficient test to determine the end behaviour of the graph of f(x).…

Q: Find the equation of the line tangent to the graph of f(x)=5x^{3}+6x^{2}-6x-3

A: This question is related to functions, We will solve it using given information.

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: Determine the equation of the vertical trace of the function g(x,y)=-x^2-y^2+2x+4y-1 corresponding…

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A: we have been given  f(x) = -x2 + 14x - 106 we have to tell the minimum and maximum value . also we…

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

A: I am attaching image so that you understand each and every step.

Q: A3) Find the equation of the line tangent to the graph of f(x) = 2x3 + 8x² – 3x – 6 at x = -2.

A: 1. find the y coordinate by putting the value of x in the function. 2. Find the first derivative of…

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Q: The graph of f(x) = where these horizontal tangents occur? 2x+3x – 120x + 20 has two horizontal…

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Q: A3) Find the equation of the line tangent to the graph of f(x) = 4x³ + 7x2 – 4x – 3 at z = -5.

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Q: The slope of the line tangent to the graph of f(x) = 19 – 4x² at the point x = -9 18 8 O 152 72 144

A: Given that: f(x)=19-4x2

Q: Find the function f whose graph has slope 2x2 + 4 df dx and which passes through the point (1, 1).

A: Given: The slope of the function is, dfdx=2x2+4x

Q: Find the x- and y-intercepts of f and sketch the graph. Approximation of graph will suffice. 1) f(x)…

A: For x-intercept : put y = 0 and For y-intercept : put x= 0

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: The graph of f(x)=3xf(x)=3x  is reflected about the yy-axis and stretched vertically by a factor of…

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

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A: Given,

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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

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Q: 24. Find the point of inflection of the curve x3 – 6x2 + 2x + 14.

A: Using formula of point of inflection of the curve.

Q: Sketch the curve: f(x) = x^4 - 6x^2

A: solution:-f(x)=x4-6x2Domain=(-∞, ∞)x-interceptsy=f(x)=0f(x)=x4-6x2=0x2x2-6=0x2(x+6)(x-6)=0(x+6)=0,…

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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A: Given:- f(x) = 2x2  Line :- 6x-y+4=0 To find:- Equation of tangent line which is parallel to given…

Q: find all the values of x at which the curve has a slope of -1. f(x) = 5 +x -3x^2

A: Given function, fx=5+x-3x2 And slope = - 1 i. e. f'x=-1

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Q: The path of a diver is modeled by f(x) = - :-x² +24x+9 where f(x) is the height (in feet) and x is…

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Q: If f(x)=5x2, and g(x)=f−1(x), what is the slope of the curve g(x)=f−1(x)g(x)=f−1(x) at the point (5,…

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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: