ļim (* +4)- ƒ(x) 3. Find the derivative of the following functions using the Show all your steps. a. f(x) = x² + 4*

Q: a(1+x²) Find the derivative 1-x

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Q: 1. Find the equation of the tangent line of f(x) at the given point. f (x) = 6x – x2, (1,5)…

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Q: Using the definition of the derivative, find ƒ′(x) . Then find ƒ′(−2) , ƒ′(0) , and ƒ′(3)  when the…

A: Given that, f(x) = 3x - 7 Then we get, f'x=limh→0fx+h-fxh

Q: the derivative of the function below using the quotient rule. y = Va + 8x7

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Q: 4x - 4 if x > 2 Suppose f(x) = Find f'(2) using the definition of derivatives. if x < 2

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Q: Use the limit definition to compute the derivative of the function at  x = 6.   f(x) = 2x2 + 6x   f…

A: Given: f(x) = 2x2 + 6x       To determine: the derivative of the function at  x = 6 using the…

Q: 5a) Using the formula man = lim+)=/G2 determine the derivative/ slope of tangent for h→0 the given…

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Q: 4. Using the first derivative test to find the location of the local maxima of the following…

A: Given function is  f(x)= x^3 -3x^2 -9x-1

Q: The derivative of a certain continuous and differentiable function is given by: y = 3-x - 12-x +9.…

A: For maxima-minima, derivative of the function must be zero. That is,…

Q: 2. Use the definition of derivative to find the derivative for f(x) = x2 + 3x . | f(x +h) – f(x) lim…

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Q: Using four-step rule, find the derivative of the following functions 1.y = (3 – 5x)*

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 2 Using the definition of derivative, prove the following: (a) f'(x) = x if f(x) = x %3D

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Q: Find the derivative. h(x)=2x^3−5x^2 / x+2 You must show

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

A: Recall: To find derivative,  f'(x)=limh→∞f(x+h)-f(x)h We have, f(x)=3x2+2x

Q: Alternative Formula for the Derivative f'(x) = lim Z-X f(z) = f(x) Z - X

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Q: (a) f(x) =x² – 2r

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 4 – x² f(x) 7+ x2

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Q: using the definition of derivative to find f'(x) for the function:f(x)=4/x. How do I solve this?

A: Given problem is to find the derivative of f(x) = 4/x

Q: FIND THE DERIVATIVE OF THE FUNCTION BY THE LIMIT PROCESS. SHOW YOUR STEP BY STEP SOLUTIONS.  1.…

A: Given:  1 fx=72 gx=-33 fx=-10x

Q: poin Find the derivative with respect to x of f(x) = V2x + 6. f' (x) =

A: Given f(x)=2x+65

Q: Find the equation of the line tangent to the graph of y = r-2x at the point T= 2. Use the limit…

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Q: Find (a) lim x--4- f(x), (b) lim f(x), and(c) lim f(x). X- -4+ x- -4 for x > -4 15) f(x) = ! x + 4…

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Q: 3. Use the second derivative to find the location of all local maxima for the following function and…

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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: f(x+h)-f(x) h Use f'(x) = lim h-0 s(x) = 6x+7 to find the derivative at x for the given function.

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Q: To find the derivative of the function, we will use the formula f(x) – f(a) х — а f'(a) = lim 7x For…

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Q: (x+ Ax)-S(x) Use the definition of the derivative f'(x) = lim Ax0 to find the equation of the line…

A: Use definition of derivative

Q: Find the equation of the tangent line to the graph of the function f(x)= 2+5 z-8 at the point

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Q: f(x+Ax)-f(x) Use the definition of the derivative f'(x) = lim Ax-0 to find the equation of the line…

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Q: 1. Let f(x) =1. Using the limit definition of the derivative, find f'(x).

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Q: a. Use the definition of the derivative to show that the derivative of f(x) = 4x² - 2x+1 is 8x-2. b.…

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Q: 2. (a) Give the definition of the derivative f'(x) of the function f(x) in terms of a limit. (b) Use…

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Q: 5. By the General Power Rule, find the derivative of y with respect to x for the function y = (4x5 +…

A: Given that, y=4x5+x4-x33

Q: Use f ′(x)=limh→0 f(x+h)−f(x)/h to find the derivative at x for the given function.   s(x)=8x+3 s…

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Q: 3. Find f'(x) using the definition of the derivative. a) f(x) = 7 lim f'(x) = b) f(x) = 3x %3D

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Q: Using the definition of derivative, find f' (x) for the function Let f(x) = x-3'

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Q: find the slope of the function at given point. use the derivative feature of a graphing utility to…

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Q: 4. When finding the derivative of a fraction you have to use the Quotient Rule. 5. The derivative of…

A: 4. when finding the derivative of a fraction you have to use the quotient rule.5. The derivative of…

Q: [4] For the Basic Absolute Value function f(x) = x, (a) state its slope (derivative) function (b)…

A: The absolute value function, |x| is defined as follows. |x|=xx≥0-xx&lt;0   The graph of |x| can be…

Q: I. Use the definition of the derivative f'(x) = lim 7&+h)=Jx) to find the derivative of the…

A: Formula: limx→axn -anx - a = nan-1 Given: R(z) = 6z3+18z5-13z10

Q: 2. Use the definition of the derivative to find the first and second derivatives of the function. 1…

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Q: with the limit definition of a derivative find the derivative of g(x) = (x-1)^2 + 1

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Q: Find the derivative of the function f(x) = 3x? – - 12x – 28 by definition of derivatives f(x + h) –…

A: A function is a relation which maps each value in its domain to exactly one value in its range. The…

Q: 1. Find the derivative of f(x) = x² – 3x. Use the result to find the slope of the tangent line to…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

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Q: Use the derivative formulas to find the derivatives of the following function. Show your work or…

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Q: f(x) = 2 Lim f(x+x) - fox) AX f'(x)= 4x40 Lim AXO Lim (x+4x)² - + (x+AX)^2-x²² AX AX x= x + 2x (0x)"…

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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: