Use the definition of the derivative to find the slope of the tangent line to the graph of the given function at any point. Show you work by completing the four-step process. (Simplify your answers completely for each step.) (x) = 4x2 + 7x Step 1: f(x + h) = (Expand your answer completely.) Step 2: f(x + h) – f(x) = (Factor your answer completely.) f(x + h) – f(x) Step 3: h f(x + h) – (x) Step 4: f'(x) = lim h0 h

Q: Find the slope and the equation of the tangent line to the graph of the function at the given point.…

A: Given,f(x)= -2x +5 and the point (1-,7)

Q: x3+ 4x2-9x-36 3. у %3 4x2+28x+48

A: Solution:

Q: Find the derivative of the function and then evaluate at the given point. у 3 3x2- 2x; (- 1,5)

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Q: Find the derivative of the function by using the definition of the derivative. f(x) = /(x³ + 5x)…

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Q: Find the derivative of the function. (Factor your answer completely.) f(x) = 4x2 In 3x %3D f'(x) =

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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: Find the derivative of the function using the definition of derivative. f(x) = 2 + 4x – 8x2

A: We have to find

Q: find the derivative of the function g(x)=5x^-3+ 6x^-6

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Q: Find the slope-intercept equation of the tangent line to f (x) = 3x² – 4x + 5 at the point (1, 4).

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Q: Find the derivative of the function by using the Quotient Rule. Simplify your answer. x2. - 4x + 3…

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Q: Find the slope and an equation of the tangent line to the graph of the function at the specified…

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Q: Find the derivative of the function y=1x+2x2+3x3.

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Q: Find the derivative of 3 4x 2 - (²x - ²)² 2x You should leave your answer in factored form. Do not…

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Q: Find the derivative of h(x)= (-2x-3)7/ (4x+2)4 You should leave your answer in factored form.

A: To differentiate the given rational function (quotient) in the required (factored) form

Q: Find the derivative of the function. y = (2x – 5)*(8x² – 5)-3

A: Derivative denotes rate of change. According to product rule, ddxf(x)g(x)=ddxf(x)g(x)+ddxg(x)f(x)

Q: Find the equation of the tangent line to the graph f(x)=x^4 +2x^2 -x at x=1. Write your equation in…

A: Equation of tangent line to the curve fx at point x=a is given by y-fa=f'ax-a Given curve is…

Q: Find the equation of the tangent line to the graph of the function f (x) = /4x³ + 5 at the point…

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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 slope m of the tangent line to the graph of the function at the given point and determine…

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Q: Find an equation of the tangent to the curve f(x) = 2x2 - 2x + 1 that has slope 2.

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Q: Find the derivative of the function. y = 3√(6x2 + 1)

A: y=36x2+1

Q: Find the slope-intercept equation of the tangent line to the graph of f(x) = x2 at (-3, 9).

A: Consider the following function: fx=x2 Differentiate fx with respect to x: ddxfx=ddxx2f'x=2x…

Q: Find the derivative of the function. q=5√x³+3x q' =

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Q: find the derivative using the definition g(x) = 2x2 + 1

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Q: 1. Find the slope of the line tangent to the graph of the function defined by f(x) = 4 + 2x - x2 at…

A: As you mentioned only 1 solved

Q: Find the derivative of the function. Provide the solution in factored form. f(x) = 2x(x³ – 2)6 %3D

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Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

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

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Q: Use the DEFINITION OF A DERIVATIVE to find the derivative of the function. 2) f(x) =5x2 + 3

A: We have to find the derivative by using definition of derivative

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: Given f(x) = –3x² – x + 15, find f' (-3) using the definition of a derivative. Provide your answer…

A: f(x) = -3x2 -x +15 find f-1(-3)

Q: Use the Quotient Rule to find the derivative of the function. 3x - 7 g(x) = %3D x² - 1

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Q: The derivative of f(x) = 5lnx is

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Q: f(x) = 3x2 + 1

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Q: Find the derivative of the function y = 4x3- x2+6x-5

A: Find the derivative of the function      y = 4x3- x2+6x-5

Q: Find the derivative of the function f(x) = 2x3 – 3x by using the definition of the derivative.

A: By using the definition of derivative of a function, we differentiate the given polynomial as in…

Q: Find the value of x for which the derivative is zero. y=x3+4x2-3x-5

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Q: Find the derivative of the function. f(x) = 9x2 (x − 6)

A: We have to find the derivative of the function

Q: Find the derivative of the function. 3. 2x2 - 5 =イ 4- x %3| y' = ||

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Q: Find the derivative of the function and then evaluate at the given point. y = 2x² - 3x: (-1,5)

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Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

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Q: find the derivative of the function using only the definition.f(x)= 16x^2-3x+12

A: Initial Calculation:The variable f(x) is a function of x. The derivative of f(x) found with respect…

Q: Use the Definition of Derivative to find the derivative of y = 6x^2 + 3x.

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Q: Find the derivative of the function. f(x)=6x2(9-8x)4

A: Use the product rule of differentiation: fx=ux.vxf'x=u'x.vx+ux.v'x

Q: Find the derivative of the fractional function y=2x+1x3.

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Q: Find the derivative of the function. g(x) = ((7x^2-4)/(4x+7)^-2

A: We have to find the derivative

Q: line has a slope of f ' ( x ) = 7x -10 / 11 given that

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Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

A: Topic = Derivative