on the graph of f(x) = 54x - 2x3 where the tangent line is horizontal Find the points (Use symbolic notation and fractions where needed. Give your answer as a comma separated list or ordered pairs in the form (*, *), (*,* (, *)...) (x, y)

Q: Let f(x)=x² -3x+5. Show that the average rate of change of f (with respect to x) on an arbitrary…

A: Average rate of change = (f(b)-f(a))/(b-a) Instantaneous rate of change =f'(a+b/2)

Q: OFind the eguation of the tangent line for f(x) = 6x²-3x +a when x= 5. You may problem. use…

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Q: find the derivative of f(x) = x-3/3x+4 using the limit definition of the derivative. then state the…

A: Consider the given function as fx=x-33x+4. The limit definition of the derivative of a function fx…

Q: Find the equation of the tangent line to the function f(x)= x^3-4x at the point where x=0. Do not…

A: Here first we find the slope using the formula m=f'0 Then equation of the tangent at point x = 0,…

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A: Given the equation of the function y=4x3+x At x=-1 the value of y on the given curve is…

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Q: Let f(x)=(x-2)(x2+4x-7). Find all the points on this curve where the tangent line is horizontal.

A: The given function is f(x)=(x-2)(x2+4x-7). Since, the slope if the horizontal tangent line is zero.…

Q: Suppose that the tangent line to the graph of a function f at x=2 passes through the point (5,19)…

A: Given that the tangent line to the graph of a function f at x=2 passes through the point (5,19) and…

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Q: 1. Use the limit definition of derivative (no shortcuts!) to find the derivative of f(x) = 3x² + 2x.

A: The formula for derivative of function f(x) using limit is given by:…

Q: Find the points on the graph of f(x) = 48x – x' where the tangent line is horizontal. (Use symbolic…

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Q: Calculate the difference quotient for f(x) = 5 - x^2 at a = 4 f(x) - f(4) / x - 4 = ?   lim  f(x)…

A: Given function is f(x)=5-x2f(4)=5-42=5-16=-11 Now, difference quotient for f(x) is…

Q: find the derivative of f(x) = (x²+4)(3x³ - 2x) at the point x = - 3[ use product rule] %3D B.

A: We have to find the derivative

Q: Find the equation of the tangent line to the graph of the given function at the given value of x.…

A: Solved below.

Q: Find the derivative of the function by the limit process. f(x) = x² + x - 5 f'(x) =| 4x – 8

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Q: Find f'(x). 6. f(x) = 4x + 7x f'(x) = Compare the graphs of f and f' and use them to explain why…

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Q: Find the equation of the tangent line at (3, f (3)) when f (3) = 20 and f' (3) = 4. (Use symbolic…

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Q: given f(x)=x^2-2x use the limit defintion of derivative if f'(-2)

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Q: Find f'(x). f(x) = x5 – 4x3 + x – 1 f'(x) = Compare the graphs of f and f' and use them to explain…

A: Given :            f(x) = x5 - 4x3 + x - 1   To find : f'(x)

Q: 3. Use the limit definition of the derivative to find the equation of the tangent line to the curve…

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Q: Please help. *Find the equation of the normal line (NL) to the graph f(x)=x³-4x at x = 3. *For…

A: To find the equation of normal line to the curve

Q: Use the second derivative test (is possible) to find the relative extrema of f(x) = 3x^4 - 8x^3 +…

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Q: Find an equation of the tangent line to the graph of f at the given point.

A: The equation of the tangent line to the graph of f at a given point x0,y0 is y-y0=f'(x0,y0)x-x0…

Q: Find the points on the graph of f(x) = 6x – 2x³ where the tangent line is horizontal. (Use symbolic…

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Q: Find the derivative of the function f(x) = 10x + 12x - 6 at number 3. (Use symbolic notation and…

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Q: Find the equation of the tangent line to the graph of g(x) = f'(x) at x = -1 when f(x) = 5x³ + 2x² +…

A: Here, f(x)=5x3+2x2+2x

Q: Find the points on the graph of f(x) = 2x3 + 15x2 - 84x + 12 where the tangent is horizontal. List…

A: we have to find the points on the graph of the function f(x) = 2x3 + 15x2 - 84x + 12 where the…

Q: 12, for f(x) n(x) Estimate the slope of the tangent line at the point x (Use decimal notation. Give…

A: Given,

Q: Find an equation of the tangent line to the graph of f ( x ) = 2x2 - 10 over 2x - 2 at the point on…

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Q: Find the slope of the tangent line of the function g(x)=3-x^2 at the point (2, -1)

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Q: ve of the function using the definition of derivative. = V7- x 1 2 7-x n of the function. (Enter…

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Q: Find an equation of the tangent line to the graph of function f(x): 3 %3D x+5 at the point (2, ).…

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Q: Find the derivative of f(x) = x² + 3x – 5 -

A: From the limit definition of derivative, f'(x)=limh→0f(x+h)-f(x)h

Q: find the derivative of f(x) = (x²+4)(3x³ – 2x) at the point x = - 3[ use product rule] В I !!

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Q: 3) Use the definition of derivative (do NOT use the short cut method) to find_ƒ'(x) given that f(x)…

A: This question is based on finding slope using definition of derivative.

Q: Find the points on the graph of f(x) = 12x – x³ where the tangent line is horizontal. (Use symbolic…

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Q: Find the derivative of f(x)=x2-3x. Use the result to find the slope of the tangent line to the curve…

A: Given: fx=x2-3x To Find: The derivative of the given function and the slope of the tangent line at…

Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = 4x − 5x2…

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Q: Find a formula for a function that has vertical asymptotes x = 6 and x = 8 and horizontal asymptote…

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Q: 7)Determine the points at which the graph of the function has a horizontal tangent line. flx) x2 х-1

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Q: Find an equation of the tangent line to f at a = 9. (Express numbers in exact form. Use symbolic…

A: Topic:- limits and application of derivatives

Q: Graph the function f(x)=−4x2 and draw the tangent lines to the graph at points whose x-coordinates…

A: Given: fx=-4x2 To Find: a. Draw the tangent line to the graph at points whose x-coordinates are -2,…

Q: Find f'(x) where f(x) = 2x2 - 5x using the limit definition of derivative.

A: The given function is fx=2x2-5x. This implies that,…

Q: Find the points on the graph of f(x)=3x-x^3 where the tangent line is horizontal.  (Use symbolic…

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Q: Use the fact that the derivative of the function f(x) =- is f'(x) = to find the equation of the…

A: We need to find the equation of tangent to the graph of f(x).

Q: find the derivative of f(x) = x-3/3x+4 using the limit definition of the derivative. then state the…

A: Given            fx=x-33x+4

Q: 27. Find the derivative of f(x) = (1 + 2x²)(x – x²) in two ways: by using the Product Rule and by…

A: Derivative of the function f(x) is given by

Q: Find all points on the graph of 3x² + 4y² + 3xy = 36 where the tangent line is horizontal. y (Give…

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Q: For the function f(x) = x^2/x+1, use algebraic methods to determine the interval(s) on which the…

A: We use first derivative test to find out where function increasing and decreasing and relative…