Let fx)= 5+2x and point P= a. Use the folloƠwing definition of the slope of the tangent line at x=a to find the slope of the line tangent to the graph of f at P. f(a+h)-f(a) man lim h-0 b. Determine an equation of the tangent line at P. a. The slope of the tangent line is (Simplify your answer.)

Q: y = 3x?+1 ; (0,1)

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Q: Write an expression for the slope of the tangent line to the  curve y − f(x) at the point (a,f(a)).

A: Given: The equation of curve is: y=fx Given point is a, fa.

Q: (a) Find all the points on the graph of (x² + y? + y)2 x² + y? that have horizontal tangent line.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: Consider the given circle x2+y2=25. Obtain the slopes of the tangent to the two points in the circle…

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A: Given that the slope of the tangent at (x, f(x)) is 2x + 1.That is,

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A: We will find the required.

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Q: Find all points (c, f(c)) on the graph of f(x) = x3 −3x2 where the tangent line has slope 9.

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Q: Given that the graph of f(x) passes through the point (8,8) and that the slope of its tangent line…

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Q: 98. Find the points on the graph of y = 2x6 – x* - 2 at which the tangent line is horizontal.

A: Find the points on the graph of  y=2x6-x4-2at which the tangent line is horizontal.

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A: Slope of a function is the first derivative for the function f(x).So integrate the value of slope to…

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A: Use the fact that derivative of a curve is the slope

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Q: )Use the formula , n = lim tun Acx) -f cal, メーa find the slope of the tangent line to to at a= I lo

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Q: Find the slope of the tangent line to the graph at the given point. (4 - x)y? = x3, (2, 2) Cissoid:

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Q: Given that the graph of f(x) passes through the point (8, 4) and that the slope of its tangent line…

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Q: find the Po s at which the tang ent liae to the graph of funstion S)= x3-4x+ 5o has Slope equalta 30

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Q: Given circle x^2+y^2=25, find the slopes of the tangents to the two point in the circle where x=-3

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Q: 1 Find the two points on the curve y=- at which the tangents have as slope of -.

A: Given,            The curve y=1x at which the tangents have as slope of -12.To find : The two points…

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A: given: the graph of f passes through the point (1,6) and the slope of its tangent line at (x,f(x))…

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A:

Q: Given that the graph of f passes through the point (2,5) and that the slope of the tangent line at…

A: It is given that the slope of the tangent line at (x, f(x)) is 3-4x So we have  f'(x)=3-4x   And…

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A: we have to find the slope of the tangent line to the graph of f at (a,f(a))

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Q: at the indicated point, find the slope of the tangent to the curve c(x) = 3x^2 - 5 at (3, 22)

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Q: a) Find the points at which the tangent line to the graph of function f(x)=2x²-24x+6 has slope equal…

A: Let y=f(x) be any function, then    Slpoe at any point, m = df(x)dx

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A: Given- g(x)=67x+1 , (-7,-5) To determine the slope of the tangent line to the graph of the function…

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Q: Let f(x) = and point P = %D 2 + 3x a. Use the following definition of the slope of the tangent line…

A: Given:

Q: If the tangent line to y = f(x) at (6, 7) passes through the point (0, 5), find f(6) and f'(6)

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Q: Find the coordinates of a point on the parabola y=−x² where the slope of the tangent is 5. x+3x+4

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Q: Given that the graph of f(x) passes through the point (10, 8) and that the slope of its tangent line…

A: Solution )slop of tangent line                f'(x) = 2x + 5 Intregating both sides  ∫f'(x) =…

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Q: Find an equation for the tangent line to the graph of f(x) = x+7 at (4,23).

A: Given: f(x)=x2+7 To Find: An equation of a tangent line to the graph of the given function at…

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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: