Write the equation of the line tangent to the graph of f (x) = -3x² + 5x + 1 at x = 1 and use it to approximate f(1.2).

Q: Find an equation of the line tangent to the graph of f(x) = - 2x at (2,- 16).

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Q: Find all points of the graph of f(x) = 3x2 + 9x whose tangent lines are parallel to the line y - 57x…

A: Solution: Two lines are parallel if they have same slope.

Q: Write the equation of the tangent line to the graph of y= 8x^4-7x-1/3-x^2 at x=1 check the…

A: First we find out first derivative at x=1 which is slope of tangent line.then we use equation of the…

Q: Write the equation of the line tangent to the graph of (x) at x=-1. f(x)=2x2+7x

A:

Q: Find the equation of the line tangent to the graph of y = (x3 - 1)(x2 + 1)4 at the point where x =…

A: The Slope of the line at any point is given by the derivative of the function at that particular…

Q: Find the equation of the line tangent to the graph of f(x) = 6x° + 5x² – 4x – 7 at x = -3

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Q: What is the maximum slope of a tangent to the function f(x) -x³ + 4x - 2? ==

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Q: What is the slope of the line tangent to the graph of f (x) = 2x2e" at x = -2? Express your answer…

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Q: Find an equation of the line tangent to the graph of f(x) when x = 2: f(x) = Vx+2

A: Find the equation of line

Q: Find the slope m of the line tangent to the graph of the function f(x)=9-x^2 at point P(4,-7).

A:

Q: Find an equation of the line tangent to the graph of f(x) = at 8,

A: f(x)=4x

Q: Find an equation of the line tangent to the graph of f(x) when x = 2: f(x) = Vx +2

A:

Q: Find the slope of the line tangent to the graph of f(x)=4x^2 +2x +1 at x=1

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Q: Find the derivative of the function. F(x) = (x* + 3x² – 2)*

A: Use chain rule to find derivative of given function as shown in step 2

Q: Find an equation for the line tangent to f(x)=x3 +3x2 -2x-8, at the point where x=1

A: To find the equation of the tangent line at point x = 1 for the given curve.

Q: Find the slope of the line tangent to the graph of each function at the given point. f(x) = x3 - 2x;…

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Q: The derivative of the function f(x) = 4x-1 is

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Q: Find the points where the graph of the function has horizontal tangents. f(x) = 3x^2 + 7x - 5

A: We have to find the points where the graph of the function has horizontal tangents.…

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = 6 + In…

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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 =…

A:

Q: Determine the point(s) at which the graph of -8x f(x) 2x - 1 has a horizontal tangent.

A: Given that  f(x)=(-8x)/(√(2x-1))  The function has a horizontal tangent  To find the point at which…

Q: Find an equation of the line tangent to thegraph of f(x) =3/x at (2,3/2)

A: Given: y=fx=3x, 2,32 for finding of equation of tangent at given point we need slopem of tangent at…

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x)=3-2lnx;…

A: To determine equation of tangent line at given point.

Q: Write the equation of the tangent line to the graph of  y = (8x2 − 6x + 2)(1 + 2x) at x = 1. Check…

A: the equation of the tangent line to the graph of, y=(8x2−6x+2)(1+2x) at x=1   y=(812−61+2)(1+21)…

Q: Find the second derivative for the function f (x) = 4e . 1 - 2x3

A: Given: fx=4ex-12x3 for finding second derivative of given, we find first derivative then find…

Q: Find the equation of the line tangent to the graph of f(x) = −2x² + x + 3 at x = 1. Provide your…

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Q: Find an equation of the tangent line to the graph of the function f(x) = 2x² - 4x +5 at the point…

A: Given, f(x)=2x2-4x+5

Q: Find the slope of the line that is tangent to the 2x-3 graph of f (x) at P(3/2, 0)

A: Slope of the tangent to tthe curve y=f(x)  at point (a,b)  is given as m=f'(a)

Q: Find the equation of the line tangent to the graph of f(x) = 7x³ + 8x² – 2x – 6 at x

A: We need to find the equation of the tangent to the function f(x) = 7x3+8x2-2x-6 at x=—2 We know that…

Q: Determine the equation of the line tangent to the graph of f ( x ) = 3 x 2 − x + 4 at x = − 1.  Give…

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Q: Find the equation of the secant line on the graph of the function f(x)=7x2 between the points where…

A: take x=-1 . take x=5

Q: What is the maximum slope of a tangent to the function f(x) = −x3 + 4x − 2?

A: Maximum slopes of tangent to function is 4.

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: Find the slope of the line tangent to the graph of f(x) = -1₂ at x = 3. x+2 Provide your answer…

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Q: Find the equation of the line tangent to the graph f(x)= (lnx)5 at x=5

A: First find slope then use equation of tangent tangent line

Q: Write the equation of the line tangent to f (x): x2 – 3x + 5 at the x

A: To find an equation of the tangent line of f(x)  at the point x=0

Q: Find the equation of the line tangent to the graph of f(x) = x² + = - 9 at x = 7. y = help…

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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: Determine the equation of the tangent to the graph of y = x³ - 3x² + x+ 3 at the point x = -1

A:

Q: Find the slope of the line tangent to the graph of f(x) = 3x² - x- 5 at x = 1.

A: The equation of the curve is given by fx = 3x2-x-5 The point is x = 1 Formula Used: mtan = dfdxx=1…

Q: Find an equation of a line that is tangent to the graph of f(x) = x³ -3 and Perpendicular to the…

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Q: Determine an equation for the tangent to the curve f(x) = 2x3 + 6x2 - 2  at x = -3

A: Given query is to find the equation of the tangent.

Q: Find the point where the tangent to the graph of f(x)= -x^2-6 is parallel to the line y=4x-1

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Q: Find the derivative of the function f(x) = x2 -8x +9 at the number a

A: The given equation is f(x)=x2-8x+9 The derivative of the function is the rate of the change in the…

Q: Find the equation of the line tangent to the graph of f(x)= x2 over (3x-4)3 at the point…

A:

Q: At what point does the graph of the function f(x) = x³ – 3x has horizontal tangent ? Find equations…

A: a) Points are (1,-2) and (-1,2) b) Lines are y=-x-1, and y=-x+3

Q: Find an equation of the line that is tangent to f(x)= x^3+2 and parallel to the line 3x-y-4=0

A: Given f(x)=x3+2

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: Find the equation of the line tangent to the curve f(x) = 4x² - 6x +39 at x = 1.

A:

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: