Prove that the function f(x) = x3 – 6x2 + 15x - 18 is strictly increasing on R. %3D

Q: Consider the function f(x)=xe−9x,0≤x≤2. On this interval, ff has a minimum value equal to: which is…

A: Given fx=xe-9x 0≤x≤2

Q: Find the function h given h'(x) = ÷- + 2; h(1) = 0 3x x2+1

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Q: Find the maximum and minimum values of the function f (x) -3x on the interval 1+x2 0<x<6.

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Q: 12. For the function f(x) = x² + 10x + 7, x ER, find any global maxima or minima points

A: If y=f(x), then the independent variable x is called the input of the function and the dependent…

Q: Find the linearization L(x) of the function f(x) = x^3/4 at x=256.  L(x)=?

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Q: On which interval(s) is the function f(x)=(12/5)x5-3x4-8x3+5 increasing?

A: Given function is,

Q: | find the Purpose of the function 十1→×>! O fn. 3メ- ,Xく! Xく1 2 f(め 2

A: Function, in mathematics, an expression, rule, or law that defines a relationship between one…

Q: Find f′(x) and f′(c). Function f(x) = (2x2 − 3x)(9x + 4) Value of c = −1

A: f(x) = (2x2 − 3x)(9x + 4) c = −1   f'(x) = (2x2 − 3x).(9x + 4)' +  (2x2 − 3x)'. (9x + 4)        =…

Q: Let h(x) = f(z) where f(x) = ln(3x² + 2x +2) and g(x) = -2x. What is h' (x)?

A: hx=fxgx=ln3x2+2x+2-2xf(x)=ln3x2+2x+2 Differentiate f with respect to x…

Q: 1) Let f(x) = –2x² – 3x + 2 f (x+h)-f(x) Find where h # 0 and simplify your answer as much h…

A: We have to find the value of function

Q: ) Find the values of the constant a so that the function f (x) will be continuous for all x. fax +…

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Q: Show that a cubic function f (x) = x3 + ax2 + bx + c is increasing on (−∞,∞) if b &gt; a2/3.

A: Given function is: fx=x3+ax2+bx+c Then we get, f'x=3x2+2ax+b

Q: 1. a) If f(x) = x-2x + 1 and g(x) =1, find f( g(-2) %3D

A: givenfx=x3-2x+1  and gx=1x2

Q: find a formula for the linear function f(x) that satisfies f(5)=7 and f(0)=-3

A: Given information:f(5)=7 and f(0)=-3

Q: Let h(x)=f(x)g(x). If f(x)=ln(3x2−2x−4) and g(x)=3x−1, what is h′(x)?

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Q: find a general formula for f (n)(x). f (x) = x2e x

A: The first derivative of a function when equated to 0 gives us the critical points of the function…

Q: The function fis increasing on the interval (s) (A) 0 1 © x>2 D x 2

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Q: The antiderivative of the function f(x) = -+ 1lx is x2 -5 + 5.5x2 + c -5 5.5x2 + c -11 + 2.5x2 + c +…

A: We know that, The expression to calculate the antiderivative of the given function: Fx=∫fxdx The…

Q: Show that the real-valued function f: R → R defined by f(x) = x° x E R. 3x2 + 3x + 1 increases for…

A: Answer

Q: Let x2-2x-3 f(x) = キ3 if For what Values of x is f Contin uo4s? Find the absolate min values of the…

A: Given function is

Q: The function x2 f(x) = 1 - x is decreasing on (0, 1). Select one: O True O False

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Q: Find the value of k so that the function 5x+3 if x<3 f(x) =. kx2 if x 23 is continuous everywhere?

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Q: If f(x) =3 ln x and g(x) = e2 , find go f(x). %3D

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Q: Let h(x) where f(x) = In(3x² + 2x + 2) and g(x) = -2x. What is h'(x)?

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Q: Find the largest interval on which the given function is increasing.

A: Consider the function fx=x-2+1 Since, fx=-x-2+1    when x&lt;2x-2+1        when x&gt;2=-x+3    when…

Q: Find the linearization L(x) of f(x) 5x2 5x + 5 at x х — 2. a) L(x) 15x 15 O b) L(x) 25x + 15 c) L(x)…

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Q: Find the linearization L(x) of the function at a. f(x) = x4 + 6x2, a = −1

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Q: Find the most general antiderivative of the function. f(x)= 8x-11/10

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Q: Find the value for k so that the function will be continuous at x = -1. S 9x - 18 l-x² - 4x – 4 + k…

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Q: let f(X)=5x +(-3) find the largest & sothat [fx)-F(a]]<E when(x-a/<8

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Q: . If x is large, which function grows faster, f1x2  2xorg1x2  x2?

A: To determine for the large values of x, which of the functions f(x)=2x and  g(x)=x2 grows faster.

Q: The function f(x) =x -x² – 2x – 1 is increasing over: %3D

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Q: f(x) = x^3 -1000x +2022 How many local minima does this function have? are inflection points of…

A: Given function f(x)=x3-1000x+2022

Q: Show that the function f(x)=x3−3x2+6x−1 is strictly increasing on R.

A: Let us find f'(x) using the power rule

Q: Q1: Find the value of the constant K if the function 4-x ;x#2 f (x) ={3-Vx² +5 is continuous at x=2.…

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Q: Find the range of f(x)=x-5x+6. O (-00, 1/4] O -1/4, co) O (-00, 00)

A: Range of Quadratic Functions Graphically : The range of a function y = f(x) is the set of values y…

Q: How do I solve this

A: We have to find

Q: f(c) {}} [=+3 = < (3x + 1

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Q: Find the linearization L(x) of f (x)=- Vx -5 at a =3. – 5 2.

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Q: Let h(x) = f(x)g(x). If f (x) = 3x² – x – 4 and g(x) = -x² + 2, what is h' (-1)?

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Q: Find G'(x). In(9) G(x) = (4e- 7t + 1) dt G'(x) =

A: Given query is to find the derivative of the expression.

Q: If f(x) = x² find a ō such that 0 < lx - 21 < & implies 1x² - 41 < F when = 1.

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Q: Find the value for k so that the function will be continuous at x = 2. 4x2 – 12x + 8 6 if x 2

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Q: Find the linearization at x = a. 1 f(x) = = 5 +3

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Q: 6) Find the value of c such that {0, c} is 2-cycle such that c be a constant and let the function be…

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Q: Compute f(x) and f(x) dx for the function f(x) = ∞  ∑…

A: f(x)=∑n=0∞x2n2n !.....(1)This is the well known series of the cosh(x)cosh(x)=∑n=0∞x2n2n !Now as we…

Q: What is the domain of the function f(x) = %3D 5" Vn n-1

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Q: f(x) = v x² + 5x - X

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Q: n x(0)=0

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