Given that f(x)=1/(x^2-4) and the derivative is =-2x/(x^2-4)^2 , use methods of calculus to: a)use interval notation to identify where f(x) is increasing and b)use interval notation to identify where f(x) is decreasing and c) find all relative max/min points (both x and y values), if they exist.

Q: 13. f (x) = sinx3 (2х-1)2

A: I have stated the used formulas in the solution

Q: Find the derivative by the limit process. x) = 11 -x

A: Given, f(x)=11-x2

Q: Determine the derivative of the cube root function f(x)=3√x using the limit definition.

A:

Q: According to the criterion of the first derivative, the image function has a point: f(x) = x2 + 10x…

A: The given function f(x)=x2+10x+21

Q: 8. Find the derivative of f (x) = 2tanx – 3secx. Show all steps -

A: We have to find the derivative of the function fx=2tanx-3secx Then,…

Q: Solve for the derivative of the function using chain rule. 9. f(x)= esinx

A: Solve for the derivative of the function using chain rule. 9. f(x)= esinx

Q: If f(x)=4/x, find the derivative of f(x) at x=2 using the limit definition of the derivative at a…

A: given function f(x)=4/x we have to find a) the the derivative of f(x) at x=2 using the limit…

Q: Compute the derivative using derivative rules that have been introduced so far. y = (x 4 + 5)3

A: Given equation is y=x4+53 Applying derivative with respect to x: dydx=dx4+53dx Using the power rule…

Q: Find the derivative by the limit process. f(x) = 11 – x2

A: We have to find the derivative by the limit process where f(x) = 11 – x2.

Q: Find all relative extrema of the function f(x) = x* – 4x2 + 2 by using the Second Derivative Test…

A: Given, The function  fx=x4-4x2+2 We have to find the all relative extrema of the function using the…

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: 1. Find the first derivative by using the definition for f(x) = 3x² – 2x – 5, hence - find f'(-2)

A: Derivative of a function is ratio of difference in output and difference in input.

Q: Let f(x)=," 1 Use the definition (first principle) to determine the 1-x derivative of ƒ(x).

A:

Q: 1) Use the limit definition to find the derivative of the function f(x) = 3x – 5x?. Then find all…

A: Derivative of the function in terms of limit is f'(x)=limh→0f(x+h)-f(x)h

Q: Determine if the critical points of the function f ( x ) = x³ + x² - x - 2 are maximum or minimum…

A: The given function is: fx=x3+x2-x-2   As we know that; To calculate the critical point, f'x=0.

Q: Find the critical coordinates of f(x) = x³ – 3x² + 8x + 1. Then, distinguish the local maximum and…

A: Given function is  f(x) = 13x3-3x2+8x+1                 ....(1) Differentiate with respect to x , we…

Q: Find the derivative of f(x) = √x^2 + 1 at a = 2, using the limit definition (i.e. first principles)

A:

Q: 7 Let f(x) x – 9 * Then according to the definition of derivative

A:

Q: Find the derivative of f(x)=8x - 5x+2 using first principles (i.e., use the definition of the…

A:

Q: Find the critical points and apply the Second Derivative Test (or state that it fails): f (x) = x5 −…

A: f(x)=x5-x3

Q: Determine the derivative of the following functions using chain rule. 3 * 1. f (x) = (2x² – 2x + 1)…

A: 1.f(x)=(2x2-2x+1)3 2. f(x)=5x3-8x2+9x-6

Q: Use the limit definition of derivative to find f (2) if f(x) = V2x + 3.

A: Use the formula for the derivative from limit defination.

Q: Analyze the stationary points of f(x) = x2ex by applying the second-order derivative test.

A: Stationary points are occurred where the first derivative of the function becomes zero. If the Value…

Q: Consider Mean Value theorem for derivative for function f(x) 4(1-2x) in interval [0,1]. TCOS(TX) -

A:

Q: Find the x-value for all relative extrema of f(x) using the first derivative test. Specify whether…

A:

Q: 1. Find the derivative of f(x) = 3x³ + 2x using the limit definition.

A: We have to find derivative using definition.

Q: Use the limit definition of the derivative of a function to find the derivative of f(x) = 4x %3D

A:

Q: 2) Use the definition of the derivative, f'(x) = lim Ax-0 derivative of f(x) = 5x² + 3. f(x+Ax)-f(x)…

A:

Q: Let f(x)=9−(4x^2+3x). Then according to the definition of derivative

A:

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: Compute for the derivative of the function f(x)= Arctan (csc2 (3x2/3))

A: Some derivative formulas: ddxtan-1x=11+x2 ddxcscx=-cotx cscx Chain rule of derivative:…

Q: Let f'(x) = 100x(2x+3)(x-5), use the first derivative test to determine the location of the local…

A:

Q: Find the derivative of the function by the limit process. 7 f(x): x - 9

A: Given,          The function is fx=7x-9.

Q: :) Given f(x) = |x|+x, at which point does the derivative not exist? Mathematically Question 4 (-…

A: We are given a function fx=x+x and we have to find the point at which fx is not derivable. We know…

Q: Find the derivative of the function by the limit process. f(x) = 7x – 6 %3D

A: The derivative is calculated using the limit process as follows. f'x=limh→0fx+h-fxh Now, fx+h=7x+h-6

Q: Solve for the derivative of the function using chain rule. 7. f(x)= sin(e3x)

A:

Q: Find the derivative by the limit process. f(x) = 11-x²

A:

Q: Find the derivative of f(x) = arctan x In(6x? + 6x – 4) 1 1 -In(бx? + бх — 4) + arctan x- -(12x + 6)…

A: Product rule (u v )' = u ' v + u v' Formula derivative of xn=n xn-1 Derivative of arctan…

Q: Find the derivative of f(x)  =(a + 2x2) (x - x2) in twoways: by using the Product Rule and by…

A: We have given function  fx=a+2x2x-x2 At first we  will use product rule:…

Q: Find the derivative by the limit process. f(x) = 13 – x2

A: Given that: f(x)=13-x2

Q: Find the derivative of the function by the limit process. f(x) = 31 f'(x) =

A: The given function is fx=31.

Q: Find the derivative by the limit process. f(x) = 15 – x²

A: Givenf(x)=15-x2Step -1From the definition of derivativef'(x)=lim∆x→0f(x+∆x)-f(x)∆x

Q: 3) Use the limit definition of the derivative to find f' (x) if f(x) = - %3D

A:

Q: Apply the first derivative test to indentify all relative extrema. f(x) = ¹²-2x+1

A:

Q: Find the derivative of the function by the limit process. f(x) = x3 - 9x + 1 f'(x)

A: We know,f'(x) = limh→0 f(x+h) - f(x)h  by limit processHere,f(x) = x3 - 9x + 1So,f(x+h) = (x+h)3 -…

Q: 4. Use the first and second derivative to find the absolute maximum and minimum, if either exists,…

A:

Q: Using the đết of derivative, fin rivative of f(x) = x² + 2x + 2.

A:

Q: find the derivative by the limit process. f(x)=14-x^2

A: Here we find the derivative by the limit process fx=14-x2

Q: Find the local extremes of f (x) = x³ +2x+ using the first derivative test.

A: Given,         The local extremes of fx=x3+34x4 using the first derivative test.

Q: A company has identified that the revenue R for a particular product is given by the equation R(x) =…

A:

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: