Determine analytically the point (s) at which the graph of the function has a horizontal tangent. x2 1) f(x) x – 1 x2 2) f(x): x2 +1

Q: Given the function f(x) = x³ - 3x2 x – 1, determine all coordinate points (x, y) on the graph of f…

A: The derivative of the function will give the value of slope. For two value of x, f(x) will have…

Q: ) Find a function ƒ such that f'(x)= x³ +3 and such that the line y+5x O is tangent to the graph of…

A: Given, f'(x) = x3+3  and the line  y +5x =0 is tangent to the graph of f   Let's assume the function…

Q: Find a function f that has the derivative f '(x) and whose graph passes through the given point.…

A:

Q: Find f'(x) and find the equation of the line tangent to the graph of f at x = 1. x-5 f(x) = 6x-1…

A: Here given that f(x)=x-56x-1 We have to find f'(x) and also we have to find the equation of the…

Q: Find an equation for f(x) using the tangent function. f(x) = f(x) 12- 10 8. 6. 4 2 X 3 2 6. 6 3 6 -8…

A: The given graph is:   To find the equation for f(x).

Q: Let f(x) = 2x2 – 8x + 14 The slope of the tangent line to the graph of f(x) at the point (2, 6) is…

A: As we know that; The slope of the tangent line to the given curve is equal to the derivative of the…

Q: Find the point on the graph of the function where the tangent line satisfies the given condition…

A: Tangent.

Q: given the functions f(x) = -x^2 -2x + 5 and h(x) = 2/x+9, find a.) f'(x) = f(x+h) - f(x) / h b.)…

A: Given fx=-x2-2x+5hx=2x+9 a.) f'(x) = f(x+h) - f(x) / h b.) g'(x) = g(x+h) - g(x) / h c.) consider…

Q: Let f(x) = 3x² - 9x + 11 The slope of the tangent line to the graph of f(x) at the point (2,5) is…

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Q: Find an equation of the curve whose tangent line has a slope of f'(x) = 4x 14/15 given that the…

A:

Q: let f(x)=(x-9)(4x+5). Find an equation for the tangent line to the graph of f at x=12.

A: Given, The function is f(x)=(x-9)(4x+5)

Q: Find a function f such that  f '(x) = 5x3  and the line  135x + y = 0  is tangent to the graph of…

A: Consider the given derivative function f'x=5x3

Q: 5. Let f(x) = 5x4 -+ 8Vx - 3. x2 (a) Find f'(x). (b) Find an equation for the tangent line to the…

A:

Q: Use the definition of a Derivative to show that the function is not differentiable at x = 1. Why is…

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Q: Find the function f given that the slope of the tangent line at any point (x, f(x)) is f'(x) and…

A:

Q: Consider the function f(x) = x2 - 1. (a) Find f '(x) using the limit defination of the derivative.…

A:

Q: [8] Use the definition f(a +h) – f(a) f'(a) = lim h-0 h To find the derivative of the given function…

A: Given: So,          f'(2)=limh→0f(2+h)-f(2)h       =limh→ 012+h-12h       =limh→ 0-12h+2       Plug…

Q: 12. Find the equation of the tangent to the following functions at the indicated point. a) f(x) = x…

A: 12. We have to find the equation of the tangent to the following functions at the indicated point.…

Q: Let f(x) = 4x3 + + 2Vx – 7. Find f'(x). 15. Find an equation for the tangent line to the graph of…

A:

Q: Let f(x) = (x - 8)(2x +7). Find an equation for the tangent line to the graph of f = 7. at x =…

A:

Q: Let f(x) = 5x4 - -1/2+8√x-3. (a) Find f'(x). (b) Find an equation for the tangent line to the graph…

A: Given that            function f(x) = 5x4-2x2+8x-3     Now             f'(x)    =  ddx5x4-2x2+8x-3…

Q: Let f=3x^2+2 and find the values below 1) f(x+h) 2) (f(x+h)-f(x)) 3) lim h→0 (f(x+h)−f(x))/h 4) Find…

A: The given function is f(x)=3x^2+2.

Q: The function g is differentiable, and the tangent line to the graph of y = g(x) at x = –2 is y = 2x…

A: Note that the slope of the line y=2x-2 is 2. Given that the tangent line to the graph of y=gx at…

Q: B. Determine the slope of the tangent line at a given value of x. 6. f(x) = x 7. f(x) = -4x3 – 2. 8.…

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Q: Assume that the functions f and g are differentiable with f(2)=4, f'(2)=3, g(2)=-1, and g'(2)=2.…

A: Given,           Assume that the functions f and g are differentiable with f2=4,  f'2=3,…

Q: 1. Sketch the graph of the function 4x f(x) = x E (-00, 00) 1+4x² Be sure to calculate the local…

A:

Q: Suppose g(-2)=3 and g'(-2)=-4. Let f(x) = x3 + g(x). Find the equation of the line tangent to y =…

A: Given,     f(x)=x3+g(x)

Q: Assume that functions f and g are differentiable with f(- 3) = – 5, f'(- 3) = – 5, g(-3) = 4, and…

A: Given F(x)=f(x)g(x)

Q: Determine an equation for the line tangent to the graph of the given function at the indicated point…

A:

Q: B4: a) Find and classify all critical points of the function f(x) = x³ + 3x? – 12x + 5 b) Determine…

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Q: Let f(x) = 33 –x The slope of the tangent line to the graph of f (=) at the point (-5, 8) is The…

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Q: Find f'(x) and find the equation of the line tangent to the graph of f at x = 1. f(x)= (1 +5x)(3-2x)…

A: topic- derivative and equation of tangent line to function

Q: Find the function f given that the slope of the tangent line at any point (x, f(x)) is f'(x) and…

A: Given:    f'(x)=3(2x−9)2,  5,32

Q: 1 Let f(x)=- (3x – 5)² -6 and f'(x) = %3D (3x – 5) Find an equation of the line tangent to the graph…

A: The given function is: f(x)=1(3x-5)2

Q: Determine an equation for the line tangent to the graph of the given function at the indicated point…

A:

Q: 3. Consider the function 8x f(x) = + 15. - The tangent line to the graph of f at the point (6, f(6))…

A:

Q: Assume that functions ƒ and g are differentiable with ƒ(1) = 2, ƒ′(1) = -3, g(1) = 4, and g′(1) =…

A: Given,

Q: Find the x-coordinate on the graph of f (x) = x3 - 12 x where the tangent is horizontal. (A) 1, - 2…

A:

Q: Let f(x) = 25 x The slope of the tangent line to the graph of f(x) at the point (–6, – 25) is The…

A: All the answers are given below

Q: Let f(x) = Find the equation of the tangent x² +1 line to the graph of f'(x) at the point where x =…

A: Given fx=1x2+1 We have to find equation of tangent to the curve f'(x) at x=1

Q: Let f(x)=(x−7)(5x+3). Find an equation for the tangent line to the graph of f at x=11. Find the…

A:

Q: 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…

A: Simplify f''(x):f''(x)=2x2-3x

Q: Find the values of x for which f (defined below) has a horizontal tangent line f(x)=(1/3)x3…

A: To Find the values of x for which f(x) has a horizontal tangent line f(x)=(1/3)x3 -(1/2)x2 -6x+7…

Q: The equation of the tangent line for the function f(x) = -8 – 5x at a = 8 is %3D y = -5(x + 8) + 48…

A: Given that      f(x) = -8 -5x at x = 8 We have to find the equation of the tangent line for the…

Q: A graph of yY = f(x) is shown. In the same coordinate system, sketch a graph of the derivative func…

A: when a line passes through two given points, say (x1, y1) and (x2, y2).  the equation for this line…

Q: find all the values of x for which f(x) will have a horizontal tangent line f(x)=(x-4)/(x^2-7)

A: Given equation f(x) For horizontal tangent line the slope f'(x)=0

Q: Find the derivative f'(x) for the function f(x) = x² + x – 17. - O A. f'(x) = 2x – 16 В. f («) — 2а…

A: Find the derivative of f(x)

Q: Let f(x)= 1/(3x+2) find the values below 1) f(x+h)= 2) (f(x+h)-f(x))= 3) lim h→0 (f(x+h)−f(x))/h 4)…

A: Let f(x)= 1 / (3x+2)Part 1)f(x+h) = 1 / [3(x + h) + 2] = 1 / (3x + 3h + 2)

Q: Suppose f(-1) = 1, f'(-1) = 5, and g(x) = x³ f(x). The tangent line to g(x) at x = 1 is given by y =

A: The objective is to find the equation of tangent line .

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: