Suppose the function f(x) has a domain of all real numbers and its derivative is shown below. f'(x) = (x + 2)7 (x - 3)3 e(x - 4) Find the intervals where f(x) is increasing. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) Find the intervals wheref(x) is decreasing. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)

Q: Find the derivative of the function using Chain Rule. h(x) = (2x-6)-¹ (x²+3)

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Q: • Show that both of the functions f(x) = (x − 1)^4 and g(x) = x^3 −3x^2 + 3x+ 2 have stationary…

A: given functions fx=x-14gx=x3-3x2+3x+2 (A) to show both have stationary point at x=1 differentiate…

Q: Find the derivative of the function f(x) = -8x² – 18x + 23 by definition of derivatives f(x + h) –…

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Q: If f'(x) = 3+ 4x and the curve f(x) passes through the point (1, 8) i) Find f(x) ii) Find the local…

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Q: The derivative of the function f is defined by ƒ'(x) = (x² + 1) cos (x²). If f(1) = 1, what is the…

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Q: 2. FIND THE DERIVATIVE BY THE LIMIT PROCESS OF f(x)=x²-6x+5.

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Q: 2. FIND THE DERIVATIVE BY THE LIMIT PROCESS OF f(x)=x³-8x+9.

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Q: Find the derivative of: f(x) = (x3 + 2) In(x)

A: Consider the function

Q: 2. Use rules of differentiation to find the derivative of the function 5a° (x- +3) g(x) = x2 +1 Show…

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Q: Suppose the derivative of the function y = f(x) is y' = (x- 2) (x + 6). At what points, if any, does…

A: see 2nd step

Q: The derivative of f(x) with respect to x is the function f'(x) and is defined as f'(x) = lim 0…

A: To find f(x+h) replace x by x+h in f(x).

Q: find the derivative of f (x) at the designated value of x. f (x) = x3 at x = 12

A: The derivative of a function can be calculated by differentiating both sides of the function with…

Q: Use the Second Derivative Test to find the Maximum and Minimum value(s) of the function 3 f(x) x* -…

A: We have the given function as fx=32x2-4x+lnx For maxima/minima, we need to calculate f'x as…

Q: Find the derivative of the function f(x) = 3x2- 13x 25 by definition of derivatives f(x + h) - f(x)…

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: if f(x) = x²√In x² x . find the derivative of this function f'(x) A. f'(x) = B. f'(x) = c. f'(x) =…

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Q: 3) Find the derivative f(x) = xe-*In(x³) %3D

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Q: Find the derivative of the function by the limit process. g(x) = -398 g'(x)=

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Q: Find the derivative of the following function by definition (from first principle): f(x)= x/(x-1)

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Q: Where does the derivative of g(x)=(x^2)/((x^2)+3) = 0 or is undefined?

A: Given function, gx=x2x2+3

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

A: We have to find derivative using definition.

Q: Suppose the derivative of the function y​f(x) is (x-1)^2(x-5)(x-2). At what​ points, if​ any, does…

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Q: .3 Find the derivative of h(x) =In x³ + 2 x5 – et -

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Q: 1 3. f(x) = (-x4-3)2

A: Solve for the derivative

Q: 2. f(x) = V-3x+ – 2

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Q: find the function with the given derivative whosegraph passes through the point P. g'(x) = 1/x2 +…

A: g'(x)=1x2+2x,P(-1,1) Formula ∫xndx=xn+1n+1+C

Q: Use the f'(x)=limh->0f(x+h)-f(x)/h  to find the derivative of f(x)=11x2 AT x=1

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Q: Find the derivative of the function f(x) = 4x2 – 13x – 30 by definition of derivatives f(x + h) –…

A: We have to find the derivative of the given function: fx=4x2-13x-30 by the definition of…

Q: Given the function f(x) = – x° – 6x2 + 5x + 12 , use either the First Derivative Test OR the %3D -…

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Q: What is the second derivative of f(x)=−x4? at the point x=−3 Do not include "f′′(x)=" in your…

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Q: Find the derivative of the function ° (2x + 1) f(x) = In x2 – 3 -

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Q: find the derivative of g(x) = (x+5)/(5-2X) using the definition of the derivative. must show all…

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Q: Find the derivative of f(x) = arctan x In(6x? + 6x – 4) - 12x 1 1 In(arctan(x)) + In(6x² + 6x – 4)-…

A: The given function is fx=arctanxln6x2+6x-4

Q: Find the derivative of the function. g(x) = In(x – 5.1x=1) g'(x) =

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Q: Find the derivative of the function. 9x + 1 h(x) = In 4х - 2. h'(x) =

A: Solution: The objective is to find the derivative of the given function

Q: 3. Find the first derivative of the function f(x)= 2x3-4x+1 using forward Difference formula if, X1…

A: Solution:

Q: Find derivative of q=(X^2-x+1)/x+1

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Q: Suppose the derivative of the function y=f(x) is y’=(x—1)^2(x—2). At what points, if any, does the…

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Q: 2) Find the derivative of g(x) = 4x^2−3x+5 using the limit process.

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Q: Find the derivative of the function.

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Q: Find the critical points of the following function. f(x) = 3x² + 5x - 1 What is the derivative of…

A: The given function is: fx=3x2+5x-1 To find the critical points of this function, equate its…

Q: Find the derivative of f(x)= 11x^2 at x=1

A: Given:    f(x) = 11 x2  at x = 1

Q: Compute the derivatives of the given function. f(x) = (2x+3x-)(2x²-3x-) a -444 Find the first…

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Q: 3- Suppose that the second derivative of the function y = f(x) is y" = (x + 1)(x - 2). For what…

A: 1)y'' = (x+1)(x-2)2)y' = (x-1)2(x-2)(x-4)

Q: Find the derivative of the function f(x) 3x2 – 12x by the definition of derivatives f(x + h) – f(x)…

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Q: Find the derivative of y with respect to x. y = In(x - 4) 4 -x X-4 x+4

A: The given function is  y= ln(x-4)  We have to find the derivative of y w.r.t. x

Q: Suppose that the second derivative of the function y = ƒ(x) is y'' = x2(x - 2)3(x + 3). For what…

A: Given that, y=f(x) Second Derivative is y'' = x2(x - 2)3(x + 3). As we know that, Inflection point…

Q: Find the derivative of the following function by definition (from first principle): f(x) = x-1

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Q: Find the x-value for all relative extrema of f(x) using the first derivative test. 1+x + x² f(x) =…

A: Given: The function is  fx=1+x+x2x2+x-2   To determine: The x value for all relative extrema of f(x)…

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.