Determine whether the statement, 'Because I have two points to work with, I use the formula for slope, (y2 - y1)/(x2 - x1), to find the slope of the tangent line to the graph of a function y = f(x) at (a, f(a))', makes sense or does not make sense, and explain your reasoning.

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

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Q: 3. Find the equation of the tangent line to the graph of x²y? + 9xy = 162 at the point (-3, 6).

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Q: If f(x) = 9x2 – x³, find f'(2) and use it to find an equation of the tangent line to the curve y =…

A: Equation of line : y-y1 = mx-x1 where x1,y1 is the point and 'm' is the slope of the line.

Q: Determine the slope of the tangent line to the curve (;² – 2x – 8) 2 -9 R(x) = at the point where…

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Q: Find the slope-intercept equation of the tangent line to f (x) = 3x² – 4x + 5 at the point (1, 4).

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Q: Find (a) the equation of the secant line through the points where x has the given values, and (b)…

A: Given f(x)=3x2-5x+7, x=2, x=4

Q: If f(x) = 8x - x³, find f'(1) and use it to find an equation of the tangent line to the curve y = 8x…

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Q: For what value of x is the tangent line to the curve y= x² - 6x +5 horizontal?

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Q: Find the equation of the tangent line to the graph of f (x) = x² – 3 at the point (3, 6). Answer y =

A: Find the equation  of the tangent  line to  the graph  offx=x2-3   at the point  3,6Answer:We  have…

Q: If  f(x) = 7x2 − x3,  find f '(1) and use it to find an equation of the tangent line to the curve…

A: Given curve , y=fx=7x2-x3∴ Derivative of fx is                        f'x=ddx7x2-x3…

Q: If f(x) = 7x2 - x³, find f'(1) and use it to find an equation of the tangent line to the curve y =…

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Q: If f(x) = 9x2 − x3, find f '(1) and use it to find an equation of the tangent line to the curve y =…

A: Given  fx =9x2-x3  Differential both sides w.r.t x and using ddxxn=nxn-1

Q: 8. Find the slope-intercept equation of the tangent line to f(x) = 3x² – 4x + 5 at the point (1, 4).…

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Q: If f(x) = 7x2 − x3, find f '(1) and use it to find an equation of the tangent line to the curve y…

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

A: Given:f(x)=2x & point (-5, -25)To determine:Equation of tangent line to the graph of given…

Q: The equation of the tangent line to the curve 교+f -25, at (8,-12) is

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Q: Find an equation for the line tangent to the graph of…

A: Given function is fx=-2xex To find: Th equation of tangent line at point a,fa for a=2 Solution:…

Q: f(x) = 2x2 -4x +5 at the point (-1,11) %3D

A: fx=2x2-4x+5 find the derivative of fx with respect to x dfdx =ddx2x2-4x+5f'x=4x-4 Now we need to…

Q: Find the slope of the tangent line to the curve -x^2+2xy+2y^3=-10 at the point (-4,-1).

A: Slope of tangent line = dy/dx at the point (-4,-1)

Q: Given the function f (x) = xe 4*, find the equation of the tangent line at the point (-1, -e*).

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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…

Q: Show that the tangent line to the curve y = x3 at any point (a, a3) meets the curve again at a point…

A: Proof: The given curve is y=x3. Obtain the derivative of the function as follows: dydx=ddxx3…

Q: If f(x) = 9x2 - x³, find f'(2) and use it to find an equation of the tangent line to the curve y =…

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Q: Find an equation of the curve whose tangent line has a slope ofƒ′(x) = x2/3,given that the point (1,…

A: Given: f'x=dydx=x23 For finding equation of curve, we will use variable separable method So,…

Q: At what point is the tangent line to the curve y = 2x perpendicular to the line x – - 2y – 8 = 0? -…

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

A: Given: fx=x2x+8; 2,25 To find: Slope (m) and equation of the tangent line to the graph of the…

Q: If f(x) = 5x2 − x3,find f ' (1) and use it to find an equation of the tangent line to the curve y =…

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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: The equation of the tangent line to the curve x² + y² = 64, at (9,-14) is

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Q: Find the equations of the tangent lines to the graph of x2(x2 +y?) = y2 when x =

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

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Q: Find an expression for the slope of the tangent line to the graph of the given Function. 1. y= 2+ x³…

A: Our Aim is to find an expression for the slope of the tangent line to the graph of the given…

Q: The slope of a tangent for the function ,2 f(x) = x² – 8x +1 at (1,-6)

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Q: 12. (a) Use the definition of derivative to find the slope of the tangent line to the curve f(x) =…

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Q: If f(x) = 8x2 - x3, find f'(2) and use it to find an equation of the tangent line to the curve y =…

A: The given function is f(x)=8x2-x3

Q: Find the slope of the tangent line to the curve y 5x at the point (-7, 245). A 70 25 -7 -70 E) 7

A: As we know that; The slope of the tangent line to the curve at a given point Px,y is equal to the…

Q: Find the points on the curve where the tangent is vertical. x=1³-3t, y-t³-31²

A: First we find dy/dx

Q: If (x) = 8x² - x, find f(1) and use it to find an equation of the tangent line to the curve y = 8x-…

A: First of all find derivative and slope

Q: Write an equation of the tangent line to the curve f(x) = 3x/√x-4 at the point (5,15). Express the…

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Q: If f(x) = 9x2 − x3, find f '(2) and use it to find an equation of the tangent line to the curve y =…

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Q: Determine the values of p, q, and r so that the function f(x) = px° + qx² + rx will have an…

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Q: If f(x) = 9x2 – x³, find f'(1) and use it to find an equation of the tangent line to the curve y =…

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Q: If f(x) = 2x2 - ax - a, b, c ER, then a +b – c=? 4 and the equation of the tangent line to the curve…

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Q: If f(x)  = 3x2 -x3, find f'(1) and use it to find an equationof the tangent line to the curve  y=…

A: Given that, y=fx=3x2-x3      ...(1)

Q: If f(x) =3x2 -x3 ,find f ' (1) and use it to find an equation of the tangent line to the curve y=…

A: Our Aim is to write an equation of tangent line to the curve y=3x2-x3 -(i) at the point (1,2).

Q: 2) Find the slope and the equation of the tangent line to a curve: y = 3x? - 4x + 1 at x = 2.

A: The given curve is y=3x2-4x+1, we have to find slope and the equation of tangent line to the curve…

Q: Find the slope and equation of the tangent line to f(x) =4+2x at a 3 using the definition.

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Q: Find the equation of the line that is perpendicular to the tangent line to f(x) = x4+1 at x = 2 and…

A: Answer and explanation is given below

Q: Find an equation of the tangent line to the curve at the given point. f(x) = 7x2 - x³, (1, 6) y =

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