Given the function f (x) = 10 + 5x³ – 3x³, identify the interval(s) where the function is concave down (-00, -) and (0. ) (주·주-) ㅇ (0·주-) and (늘, 00) ㅇ (-t, t)

Q: Calculate the derivative. f(x) = 3ex - x3

A: Differentiation of the function with respect to x helps to find the derivative of the function.…

Q: Differentiate the function using the three step rule. Show your solution. f(x)=(x)/(√(x-4))

A: You must have idea about three step differentiation method.

Q: Which function has x-intercepts at −2π, −π, 0, π, 2π?

A: Given-  The function has its x- intercepts at -2pi, -pi, 0 , pi, 2pi

Q: Find the slope of the secant line to the function f(x)=x3 when x=1 and x=2.

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Q: Find the derivative of f (x) = x3 - 10x2 + 8 .

A: Given : fx = x3-10x2+8

Q: Use the Chain Rule to find the derivative of the function. y = (2x² - 9)3

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Q: Find the derivative of the function. f(x) = (2x3 − 8x2 + 7)6

A: Given,           The function is fx=2x3-8x2+76.

Q: Differentiate the function using quotient rule. 3x y = 2х + x2

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Q: A 400-room hotel can rent every one of its rooms at $120 per room. For each $1 increase in rent, two…

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Q: Find an equation of the line tangent to the graph of f(x) = (5x-9)(x+6) at (2,8). The equation of…

A: This question is based on application of derivative to find slope of tangent line.

Q: Find the relative extrema of the functions f(x)=-4x2-32x-62. Identify any maximum or minimum by…

A: Given function is Differentiating f (x) with respect to x, we get Now, we will find critical…

Q: Calculate the derivative. f(x) = x 3/2(2x 4 - 3x + x - 1/2)

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Q: Using the second derivative criterion, find the graphs of the functions a) F(x) = x*– 8x² +3

A: Given- (a)  Fx=x4-8x2+3 To Find- The graph of the above functions using second derivative.

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

A: Givenfx=3x4−18x3+x−7

Q: Use the deffinition of derivatives to deffrintiate y= -x3+3x-6

A: Here the given function is

Q: Using derivative, find the absolute maximum and minimum of f(x) = 2x3 +3x2 −12x on [−3,3]

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Q: Find the third derivative. f(x) = 4x9 − 7x6

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Q: Use the Chain Rule to find the derivative of the function. y = (3x2 - 7)3

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Q: Find the point at which the line f() = --1 intersects the line g(a) 2 + 8

A: Two lines f(x)=-x-1 and g(x)=2x+8 , we have to find the point at which both lines intersects.

Q: iven the function y=2x³-4x²+5,

A: Given, the function               y=2x3-4x2+5

Q: check uniquness and existance for fixed point while f(x)=(2x+1)^-3 in [1,2]

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Q: Find the slope of the line tangent to the graph of the function defined by f(x) = 3x2 – 4 at (1,…

A: Solution:Given        f(x)=3x2-4   at (1,-2)To find:Slope of the line tangent to the graph The…

Q: Find the derivative of the function. f(x)=6x3 − 7x2 + 2/x3 − 3

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Q: The domain of the function f(æ) = v9-a is OR-{-81,81} OR-{-7,11} O R-{-9} OR O R- {9}

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Q: Compute for the possible root of the function f(x) = x4 - x³ - x? - 4 in the interval [-2, -1]. Use…

A: The equation in the form f(x)=0 is called a transcendental equation. If the function is continuous…

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

A: Solve for the derivative

Q: Find the slope of the line tangent to the graph of the function defined by f(x) = x2 – 3x + 4 at…

A: It is given that, f(x)=x2-3x+4   Slope of any function or tangent of any function is defined as the…

Q: Using appropriate rule, find the derivative of 8x+4 Y= 4x²+6æ+8 4.x24

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Q: For the function, find all critical numbers and then use the second-derivative test to determine…

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Q: B. Apply the quotient rule to find the derivative 1. y 4-7x 3. y = 5- 3x

A: From the quotient rule of derivative we get Let,  y=uv where u and v is function of x then dydx=…

Q: Find the range of the function y = -4(x – 3)2 + 4. O (-∞, ∞) O (-∞, –4] O [3, ∞) O (-∞, 4) O [-4, ∞)…

A: Range of function :  The set of all values of the dependent variable for which a function is defined…

Q: 3x y = 2х + x2

A: The given function is y=3x2x+x2 quotient rule: fg'=f'·g-g'·fg2

Q: How will you differentiate an implicit function that can't be expressed in the form of y = f(x)?

A: For the differentiation of implicit function, we will differentiate each side of an equation with…

Q: Find the derivative of the function. y = 5x3 − 7x2 + 9

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Q: The derivative of f(x) = (2x - 1)/(x2 + 1) is (-2x² + 2x + 2)/(x4 + 2x² + 1) Select the correct…

A: Derivative of the function

Q: Using the definition of the derivative, differentiate the function f(x)=x2+2x−2.

A: To find the derivative of the function f(x)=x2+2x-2 By the limit definition of the derivative,  The…

Q: -4 - Find the derivative for the function f(x) = (5x−4+ 3x + 7) (8x−³ − 7x + 10) 5. Do not simplify…

A: Given, f(x)=5x-4+3x+78x-3-7x+105

Q: use the second derivative test to find and characterize all the relative extremes of f(x)=2x4-24x3+4

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Q: Find the domain of the function. 4) f(x) = x2 + 3 A) (-«, -3) u (-3, ∞) C) (-3, «) 4) B) (-*, «) D)…

A: We will find out the required domain.

Q: For function, find the point in the graph at which the tangent line has slope 9 Y= -0.025x^2+6x What…

A: The given function is:Y=-0.025x2+6xThe slope is 9

Q: for the Function Fc)-, find %3D

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

A: Given function,  f(x)= 3x4 − 18x3 + x − 5 The function f(x) is concave upward on an interval I if…

Q: Find the derivative. f (x) 7.) f(x)==x³+2x²–11 x–1 +2x²-11 x-1 6.

A: We have given

Q: Differentiate the function. y = (2x* - -x+1) (-x* +3) y' = D

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Q: find the derivative  f(x)= (x1/3-5)(x2/5-3x1/5+4x-1/3)

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Q: Rewrite the function g(x) = ((x^2)-1)/((x^2)+2) so that you can solve for the derivative using the…

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

A: GIVEN

Q: Suppose for a company the function of income (in dollars) is given by R(x)=-0.12x^3+1,296x+12201…

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Q: Find the derivative of the function using chain rule. f(x) = (4x5 – 2x*)10

A: We differentiate the given function by using chain rule, see attached file for a step by step…