Evaluate the function at the given values of the independent variable and simplify : f(x) = x/lxl , a. f(6) b. f(-6) c. f(r2).

Q: f(x, v) = a² + y² - 4zy.

A: We have given f(x,y)= x2 +y2 -4xy Now, for finding the critical point we have to find partial…

Q: Differentiate the function with respect to the independent variable. f(x) = %9+ 3x? %3D f'(x) =O

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Q: Where is the function y=(x−5) 3 concave down?

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Q: Find the simplified difference quotient for the given function    dx2 + kx + m

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Q: Find and simplify the function values. f(x, y) = 8x + y2 Exercise (a) f(x + Дх, у) — f(x, у) Дх

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Q: For the function f(x) = V - 6, find f-(x).

A: Given : f ( x ) = x ( 1/4)  - 6  find : f - 1  ( x ) = ?

Q: For the function f(x.y) = e 4xy, find f, and f,. f, =

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Q: f = y/x

A: Given function f=yx The gradient of the function f(x,y) is given by ∇f=∂f∂xi^+∂f∂yj^.

Q: -4x For the function f(x) = e¯X+4e*, then f(x) = %3D

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Q: Find for Domain and Range of the function f (x,y) = /49 – x2 – y²

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Q: Given the function f(x)=0.2(x−2)(x+1)(x−5), determine the end behavior of the function

A: Given the function,

Q: For the function f(x,y) = 5y + x, find f(3, – 5), f(- 1,4), f(- 3, – 4), and f(0,7).

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Q: For the function f(x) = 3 (e - 8) + 2, find f(x).

A: Given f(x) and inverse of f(x)

Q: of the function f(x) = 3x from x, =0 to x, =7. (Simplify your answer.)

A: We have to find

Q: For the function f(x,y) = 8x² + 7y², find f(x + h,y)-f(x,y) = h f(x + h,y)-f(x,y) h

A: Given, f(x,y)=8x2+7y2

Q: Find The difference quotient f(a+h)-f(a) where h 0. f(x) = X h x +4

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Q: The depth in feet, D, of a scuba diver can be modeled by the function D(x) = -ř + 12r + 4, where x…

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Q: For the function f(x)= 4 e , find f"(x). Then find f"(0) and fP"2).

A: Take derivative with respect to x.

Q: Given the piecewise function defined below, determine the value of f (x)dx in simplest form. -6x² +…

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Q: For the function y = f(x), find f'(a)

A: Here we have, f(x)=x2+5x+2; a=-3 We have to find f'(a)=?

Q: For the function f(x,y) = 7x² + 6y², find f(x + h,y)-f(x,y) = h f(x+h,y)-f(x,y) h

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Q: What is the y-intercept of y = Vx+1+3? Explain using transformations of this function from the…

A: Given that  y=√(x+1) +3 To find the Y-intercept of y

Q: find the value of the constant (a, b, or c) that makes the function continuous. (x2 - c 4x + 2c for…

A: For limits to be continuous left hand limit must be equal to right hand limit and equal to limit at…

Q: Sarai was given the function, f(x)=x² - 2x +8. For what x value(s) would f(x)= 20?

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Q: For the function f(x,y) = 3x2 + 7y2, find the following. f(x +h,y) – f(x,y) а.

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Q: V, find f(x). 9 For the function f(x) =

A: Given f(x)=9x54 and i.e. y=9x54Now we swap x and y to find the inversex=9y54 and here solve for y

Q: For the function f(x) = vx – 2, find f'(x).

A: Given,           The function is fx=x-2 .

Q: Express the function in the form   f ° g  ° h

A: The given function is Rx=x-1 It is required to show the given function in the form of fogoh. So,…

Q: dx Find for the following function. 3at? y= |+t5 3at X =

A: The objective  of the question is find the derivative of the function.

Q: For the function y df-1 f(x) = a? – x + 2, x > 0.5, find dy y=10 (f-1)'(10).

A:

Q: Find the range of the function f(x) = x2-1 O [-2,21 R\[-1] R\{0}

A: Range of function

Q: Use the function to evaluate the indicated expressions and simplify. f(x) = x + 6 f(x²) = %3D…

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Q: Find the value f(3) for the function f(x)=9

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Q: Differentiate the functions. ?????? ?????????? ??  y=(1+t)²/t²

A: given function       y = (1+t)2/t2

Q: For the function f(x) = x^2/2-x, what is f(a+h)?

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Q: For the piecewise function, find the specified function value. forx s-1, 3x, f(x) = { %3D x- 6,…

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Q: For the function f(x,y) = 5x² + 6y², find f(x + h,y)-f(x,y) h 11 f(x + h,y)-f(x,y) h

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Q: For the function f(x) = x3/3-x2- 24x + 19. what is the value over which the function is concave…

A: fx=x33-x2-24x+19    Now, first derivative is  dfdx=ddx(x33-x2-24x+19)  dfdx=x2-2x-24    And, second…

Q: Differentiate the function with respect to the independent variable. f(x) = 2x° In xº f'(x) =O

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Q: Find the inflection point (x,, f(xp)) of the following function: f(x) = 3x³ + 9x² – x + 11. If - an…

A: Given : f(x) = 3x³ + 9x² - x + 11

Q: Determine where the function is concave upward and where it is concave downward. (Enter your answer…

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Q: Determine the value of a, when f(x) = e“ + xand f'(0) = 3.

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Q: For the function: f(x) = 2x + 8, f(æ) – f(a) с — а -

A: Given that f(x) =2x+8 .First we evaluate f(a) then substitute in the given expression.

Q: Find f"(0) for the function f (x) = – 2xe-x Answer:

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Q: Find and simplify the difference quotient f(a + h} – f(a) for the function. (x) = 5Vx

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Q: Find the inflection point(s) of the function f(x) = 3e¬x. %3D (х, у) %3D (smaller x-value) (х, у)…

A: Given,  f(x)=3e-x2

Q: Find  f' in terms of g' .

A:

Q: Given f(x)=e^x+1/3x, find f'(8)

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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: