Given the function f(x) = x³ - 3x2 x – 1, determine all coordinate points (x, y) on the graph of f such that the line tangent to f at (x, y) has a slope of -1.

Q: Find all points on the graph of f(x) = x +a where the tangent line is parallel to the line y = 28x.…

A: Consider the function f(x) = x3 + x Slope of the tangent to f(x) is the derivative of f(x). f'(x) =…

Q: Find all points (x, y) on the graph of g(x) = x3/3 -3x2/2+1 tangent lines parallel to the line 8x -…

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Q: Given f(x) (x – 4)(-5x – 3), find the (x, y)-coordinate on the graph where the tangent line is…

A: For coordinate of horizontal tangent line  Differentiation of given function Finding critical point…

Q: 5. Find using first principles the slope of the tangent to f(x) = x² + 6x + 9 at x = -3.

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Q: Find all points (x,y) on the graph of f(x) = 2x3 + 1 with tangent lines perpendicular to the line y=…

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Q: (a) If F(x) = 6x/(2 + x2), find F '(2) and use it to find an equation of the tangent line to the…

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Q: Find all points (x, y) on the graph of f(x) = x - 3x + 8x + 23 with tangent lines parallel to the…

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Q: Find an equation of the secant line containing (1, f(1)) and (2, f(2)). f(x) = x² - 2x

A: Rule:-equation of line passing thraught (x1,y1) and (x2,y2) is y-y1=y2-y1x2-x1(x-x1)

Q: find the point (x,y) at which the graph of y=7x2+5x-6 has a horizontal tangent line.  The function…

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Q: Find f(x) if f(0) = 0 and the tangent line at (x, ƒ (x)) has the slope x(x² + 2}°.

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Q: The slope of a tangent to the curve f(x) = x² + 2x – 5 at the point (3, 10) is : 12 8. -5 10

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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: 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 equation of the tangent line to the graph of the function f(x)=(x2+7)(x−2)fx=x2+7x−2 at the…

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Q: Find a function f such that f'(x) = x“ and the line 2a - y = 3 is tangent to the graph of f. り

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Q: . Find all points (x, y) on the graph of f(x) = x with tangent lines passing through the point (3,…

A: Tangent line has an equation of line with slope equals to derivative of the function at that point.…

Q: Find the slope of the line tangent to the given curve at the indicated point. a. f (x) = 3x + 10 at…

A: Given function,f(x)=3x+10,Aim:- To find the slope of the tangent of the curve f(x) at (-3,1)Let…

Q: f the line tangent to the graph of y =x* – 2x + 1 at x =-1

A: Idea: find the slope of tangent line by differentiation at x=-1 .then find the point on the curve.…

Q: Find all points (x, y) on the graph of f(x) = x° - 4x + 20x + 11 with tangent lines parallel to the…

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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: Find the equation of the line tangent to the graph of f(x)=−3cos(x) at x=−π3

A: As we know that: The first derivative of the function is equal to the slope of the tangent line to…

Q: the line tangent to f(x)=x' 3.

A: we have to find the equation of line tangent to  f(x)=x3-x2-5      , at the point (2,-1)

Q: 4. Find the slope of the line tangent to the graph of 1 f (x) = 2x4 – 32x3 + 17x2 – 9x + 4 at x 2 -…

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Q: Find f(X) if F(0)=0 and the tangent line at (x,f(x)) has a slope X(x^2+2)^3

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Q: Find an equation for the line tangent to the graph of f at (3, 103), where f is given by f(x) = 5x³…

A: As we know that; The expression for the equation of the tangent line is: y-y0=mx-x0 Where m is the…

Q: Find the point (x,y), at which the graph of y = 8x+6x-3 has a horizontal tanger The function y= 8x…

A: Our Aim is to find the point (x,y) at which the graph of y=8x2+6x-3-(i)has a horizontal tangent.

Q: Find all points (x, y) on the graph of y = x/(x - 2) with tangent lines perpendicular to the line y…

A: Given:

Q: Find the derivative of the function. x3 y -1 -2x3+3x2 y's (x- 1)2 y'= 2x-3x2 (x-1)2 y'= 2x3+ 332 (x-…

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Q: Find an equation for the line tangent to the graph of f(x) = 2xe %3D at the point (a, f(a)) for a =…

A: f(x) = 2xexslope of tangent will be calculated by differentiation function f(x) at given point.f(x)…

Q: Let f(x) = 2x + 3 – 17e". Find the equation of the tangent line to the graph of f(x) at the point…

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Q: Suppose f (x) = (x 2 − 2x) (3x + 2).What is the equation of the line normal to f(i.e., the line…

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Q: If  F(x) = 12x/(3 + x2),  find F '(3) and use it to find an equation of the tangent line to the…

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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: Find an equation for the line tangent to the graph of f at (1, 14), where f is given by f(x) = 30 -…

A: Please refer the attached image for complete solution.

Q: find an equation of the tangent line to the graph of f(x)= 5x^2-7 that is parallel to the line…

A: The general equation of line in slope intercept form is y=mx+c where m is slope and c is…

Q: Find the values of x at which the graph of f (x) = 4x² – 3x + 2 has a tangent line parallel to the…

A: Note : As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 8. For the function f(x) = x2 - 2, find: a) The slope of a tangent line at x = a.

A: To find the slope of tangent line at x=a.

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: 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: Let f(x) = 2x* + 3x° + 10. Find the equation of the line tangent line to the graph of Y point (1,…

A: Given  f(x) = 2X⁴ +3X³ +10 We need to find the equation of tangent of f(x) at the point (1,15)

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: For f (x) = x 3, show that the slope of the secant line over [ -3, x] is x 2 - 3x + 9, and use this…

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Q: Find the equation of the tangent line to the function f(x) -x2 – 4x + 4 at the point where x = -2. =…

A: Answer is- Option 3 is correct Explanation is given below...

Q: Find an equation for the line tangent to the graph of: f(x)= 2xex at the point (a,f(a)) for a=2.

A: Given curve Now, we find f'(x) We know that slope of tangent line to the curve y=f(x) at point x=a…

Q: Find the equation of the line tangent to f(x)=3/(2x+1)at the point (1, f(1))

A: Given function is  fx=32x+1

Q: Find all r-values where f(x) = (x2 + 2x - 3)4 has a horizontal tangent line.

A: The function f(x)=x2+2x-34. We have to find all x-values where the function f(x) has a horizontal…

Q: For the function y= In(x² – 2) , the slope of the tangent at x = 2 is

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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: