Given f"(x) = x(2x-3), find f(x) if the point (2,7) is on the curve y=f(x) and the slope of the tangent line to f at that point is 8. %3D

Q: 2. Find the slope of the tangent line to the curve y = x3 – 2x + 1 at x = 1.

A: As we know that: The first derivative of the function at a point is equal to the slope of the…

Q: Estimate the slope of the tangent line of the function f(x) = 2e* at the point x = e. %3=

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Q: 4. Find the point(s) on the curve of y=,x+x+2for which the slope of the tangent line is zero. (5)

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Q: Find the slope of the tangent to the curve y x3 at (6, 3) xy + 6 dx (Enter undef if the slope is not…

A: Given that: y2=x3xy+6 at (6, 3)

Q: For which value(s) of x does f(x)=−x^3/3−2x^2+3x−8 have a tangent line of slope 7?

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Q: Consider the graph of the function f(x) = ln(1 + x²) for x > 0. 1. Find f'(x). 2. At which value of…

A: Ta which value of x the slope of tangent line the greatest.

Q: 2. Find the equation of the tangent line to the curve y = x² – 2x - 3 that is parallel to the line x…

A: Given: The tangent line to the curve y=x2-2x-3 is parallel to the line x+y=1. To Find: The equation…

Q: 3. What is the slope of the tangent line to y = 4* at x = 0?

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Q: For f(x)=x5, the instantaneous rate of change is known to be 405 at x=-3. Find the equation of the…

A: y=fx=x5instantaneous have of change is known to be 405 ,or x = -3∴ y=f-3=-35=-243

Q: Find the point where the tangent line to y=x2 at x=0.4 crosses the x-axis. x-intercept =

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Q: Find the equation of tangent for the implicit function x3 - xy2 + 3y2 + 4 = 0. at the point (1, 2)

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Q: Find f(x) if f(2) = 3 and the tangent line at x has slope (x - 1)e** - 2x. f(x) = 1)et?

A: We have to find the function

Q: 4. Find an equation of the line tangent to g(x) = 3x² - x +1 at x= 1.

A: Given function

Q: 2. Find the equation of the tangent line to the curve y = x2 - 2x -3 that is parallel to the line x…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Find the point where the tangent line to y = x* at x 0.3 crosses the x-axis. x-intercept =

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Q: Find the equation of the tangent line at x=9 for f(x) =X^3/2

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

Q: For f(x)=x3​, the instantaneous rate of change is known to be 3 at x=−1. Find the equation of the…

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Q: Find f(x) if f(1) = -1 and the tangent line at (x, f(x)) has slope 3ex+7 f(x)= ?

A: Given:

Q: Determine the equation of the tangent line to the function y = 2 + xe³x + x when x is equal to 0.

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Q: The tangent lines to the graph of f(x) = x2 grow steeper as x increases. At what rate do the slopes…

A: The tangent line of any given function is the line which  touches the curve of function at only one…

Q: Find the points on the graph of y = ex + e-2x where the tangent line is horizontal.

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Q: 25.For which x – values does the graph of y = e3x³-2x-4x have a horizontal tangent line ?

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Q: 2 Find the slope of the tangent line to у 3 at X = 1 3 - х

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Q: 3. Find an equation of the tangent line to the curve at x=4 y=(sqrt(x)) / (x+6)

A: Given equation of the curve y = xx+6  ...............(1) Let the equation of the tangent at (x1, y1)…

Q: 4. Find the slope of the tangent line to the function f(x)= +3; x+2 at x = 4 5x-10

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Q: Find the point where the tangent line to y = x² at x 0.7 crosses the x-axis.

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Q: Fin the equation of the line tangent F(x) = xcos(x) + e^x at the point (0,2)

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Q: Find the equation of the tangent line to y = 3e at x 7.

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Q: 8. Find the point on the graph y = x³ where the tangent line is perpendicular to the line 3x +9y = 4

A: We have to find the point where tangent line is perpendicular to the line 3x+9y=4.

Q: A line with slope m passes through the origin and is tangent to the graph of y = ln x. What is the…

A: Let the point of contact is (h,ln(h)) We find the slope of the tangent using dy/dx

Q: 2. Find the slope of the tangent line to f(x)=V4-V+5 at the point where x 4.

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Q: Find the equation of the line tangent to the graph of y = (x2 - x) ln (8x) at x = 2

A: Topic = Derivative

Q: Find the slope of the tangent to the curve y2 ln(x) + x2y = 7 at (1, 7)

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Q: Find the slope of the line tangent to the curve y = sin' x at the point where x-x/3

A: We have to find the slope

Q: 3. FIND THE SLOPE OF THE TANGENT LINE TO THE GRAPH OF 5x + 2xy + 4y² = 25 AT THE POINT (1,2).

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

Q: Near x=0, the tangent line approximation gives 4e^(-4x) ≈

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Q: 2) Find the equation of the tangent line in slope intercept form to the curve x² + 4xy + y2 = 13 at…

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Q: 5. Find the slope of the tangent line to the graph of r = 2-2cos e when 0 = に一2

A: We have given equation of graph r=2-2cosθ  We have to find slope of the tangent line to the graph…

Q: -1 Where on the curve Y (1+ x2)¯ does the tangent line have the greatest slope? NOTE: Enter the…

A: Given:- y = (1+x2)-1 To find:- Point where tangent line on given have greatest slope

Q: Find the point where the tangent line to y = 5x at x = 0.5 crosses the x-axis.

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Q: The tangent lines to the graph of f (x) = x2 grow steeper as x increases. At what rate do the slopes…

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Q: 6. Find the equation of the tangent line to the curve y = e when it is parallel to 2x- y=7.

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Q: 9. Find the point on the graph of y = x² where the tangent line is parallel to the line 3x – 4y = 4.

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Q: 9) Find the equation of the tangent line to: y = (1+x) e*when x=0

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Q: The slope of the tangent line to the curve y=2e10xcos(-6x) at x-0 is

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Q: 3. FIND THE SLOPE OF THE TANGENT LINE TO THE GRAPH OF 5x + 2xy + 4y² = = 25 AT THE POINT (1,2).

A: Given: 5x+2xy+4y2=25

Q: find the slope to the tangent line x^2e^4x at the point (-1,e^-4)

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Q: x =t - sint y = 1- cost

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Q: Find the equation of the tangent line to the curve at the point (5,3) given that x2+xy+2y2=58

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Q: Find the x-coordinate of the point on the graph of y=x^2 where the tangent line is parallel to the…

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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: