Suppose that the function f is defined, for all real numbers, as follows. if x<-1 f(x) = -(x+1) if -1sx<2 1 if x22 Find f(-5), f(1), and f(2). f(-s) = 0 s(1) = 0 %3D s(2) = 0 %3D

Q: Suppose that the function f is defined, for all real numbers, as follows. if x<-2 f(x) =< - (x-1)²+2…

A: The given data in the question is -                                                 f(x) = 3 if…

Q: Suppose that the function f is defined, for all real numbers, as follows. 3x-1 if x<-1 f (x) =- -x+1…

A: Given: The Piece wise function f(x)=-3x-1If x&lt;-1-x+1If x≥-1 To find: Graph the given piece wise…

Q: Suppose that f is a differentiable function such that f(4)=4 and f'(4)=-2. Let g(x)=f(xsquare root…

A: We first find g'(x) and then evaluate g'(4).

Q: Prove that the function given by f(x) =x3-3x2+3x-100 is increasing in R

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Q: Find the absolute minimums and maximums of the following function on the given intervals

A: The given function on interval [-2, 5] is

Q: Suppose that the function g is defined, for all real numbers, as follows. --x²+5 if x + 1 g (x) -3…

A:

Q: Suppose that 2 <f '(x) < 4 for all values of x. What are the minimum and maximum possible values of…

A: Using Mean Value Theorm.

Q: Find the absolute maximum and minimum values of f on the given closed interval, and state where…

A: We first have to find the critical points. For that we find f'(x). Then set f'(x)=0 and solve for x.…

Q: Find f such that the given conditions are satisfied. f'(x) = x - , f(0) = 8 f(x) = =x3/2 - 2x + 8…

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Q: Find the constant a such that the function is continuous on the entire real line. 7sin x 0 = g(x) =…

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Q: Find the absolute extreme values of the function on the given interval. f(x) = x4 + 8x3 + 14  on…

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Q: The function f (x) = x3-3x has: %3D Concave up for all x O Concave up for x0 Concave down for all x…

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Q: Find the value of the following function at x = 3 and x = 4. Does the Intermediate Value Theorem…

A: Given: f(x)=-x3+3x2+2x+7. Substitute x=3 and x=4 in f(x). f(3)=-33+332+23+7=13&gt;0…

Q: Suppose that the function f is defined, for all real numbers, as follows. if x1 Find f(-2), f(-1),…

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Q: The function h(x)= 1 over x-8, can be expressed in the form f(g(x)), where g(x)= (x-8) , and f(x))…

A: use composition of function to find the function f(x).

Q: Suppose that the function f is defined, for all real numbers, as follows. 4 if x2 Find f (-2),…

A:

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: Show that the function f(x) = |x - 6| is not differentiableat 6. Find a formula for and sketch its…

A: Consider the given function: fx=x-6 Here, the objective is to show that the given function is not…

Q: Suppose that f(x) is a differentiable function such that f(4)-5 and f(4)=4. If g(x)=2xf(x), then…

A: Given f(x) is differentiable function such that f'(4)=5 and f(4)=4. Differentiating with respect to…

Q: Find the constant a such that the function is continuous on the entire real line. 2sin x a 11 g(x):…

A:

Q: Consider the function f(x) = x – 18x + 3, - 2 < x < 7. The absolute maximum of f() (on the given…

A: If f(x) is a function, then the absolute maxima and minima are the points of the function where the…

Q: Suppose that the function f is defined, for all real numbers, as follows. -x+2 if x1 Graph the…

A: Follow the next step

Q: find the largest domain for f(x) = (x-3)2   with an upper x bound of 8 such that the function f is…

A: fx=x-32 Differentiating with respect to x, we get f'x=2x-3 Now function is non decreasing in the…

Q: . Find the absolute the following functions on f(x) = x² - 6x + 5 minimums the and maximums of given…

A: As per our guideline we are supposed to answer only first question of a multiple type of questions.…

Q: Suppose that f(1) = 3 and that f'(x) ≥ 4 for all x. How small could f(9) be? ( Using TheMean Value…

A:

Q: (b) Suppose f'(x) > 1 for all x > 0, and f(0) = 0. Show that f(x) > x for all x> 0.

A: We will be using mean value theorem

Q: Find all values of x for which the function f(x)=(x^2+x-6)/(x^2-5x+6) is not continuous.

A: We will solve the problem.

Q: Find the function f if it is known that f prime of x= 3x^2 +6x-7 and f(-1)=10.

A: Given: f'x = 3x2 + 6x - 7 and f-1 = 10 To find: fx

Q: 14. If f(x)= x+4 and h(x)= 4x-1, find function g(x) such that gof =h. %3D

A: Given that , fx=x+4 and nx=4x-1We have to find gx such that got=h

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: Given:-f(x)=3+3x-3x2 ; 0, 3f'(x)=3-6xfor critical pointsf'(x)=03-6x=06x=3x=36=12second derivative…

Q: Suppose that the function f is defined, for all real numbers, as follows. 1 if x 1 Find f(-2),…

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Q: ) Given the function f(x) = {6 − x        if − 1 ≤ x ≤ 2…

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Q: Consider the compound function:             (x - 2)3 for x less than or equal to 2 h(x) =  |x| for…

A:

Q: Suppose that the function f is defined, for all real numbers, as follows. x+1 if x<-1 S) = -(x+1…

A:

Q: let f: R^ -> R be a function given by 2 f(x₁, x₂... x₁) x.x²2. x²n, where = € 2.1 Show that the…

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Q: Find the absolute minimums and maximums of the following function on the given intervals

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Q: Suppose that the function h is defined, for all real numbers, as follows. --x²+5 if x # -1 h(x)=< 4…

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Q: ind the intervals on which the function f(x) =x2 +5x2 -8x+1 is strictly increasing function

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Q: Find the absolute minimums and maximums of the following function on the given intervals

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Q: Let f(x) = 1 and 1 if x > 0 g(x) 8 +- if x < 0 Show that f'(x) = g'(x) for all x in their domains.…

A: Given,The function g(x)=1x Consider only the case when x&lt;0 because already know that f(x)=g(x)…

Q: If the function f is continuous for all real numbers and if f (x) = when z# -2, then f (-2)= -4 B -2…

A: we will use the fact that f is continuous for all real numbers and hence we will use the definition…

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A:

Q: Suppose that the function h is defined, for all real numbers, as follows. h(x)=< 3 if x=-1 -4 if…

A: Topic = Function

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

A:

Q: Suppose that f(x) = x*, x 2 5, and that g(x) = Vx + 3, x > 5. Find a formula for (f • g)(x) and find…

A: fx=x4, x≥5  &amp;  gx=x+3, x≥5 Now, f∘gx=fgx=fx+3=x+34=x+32

Q: Let f be a real-valued function on R. Suppose that f(−1) = 3 and f'(x) ≤ 2 for all values of x. How…

A: f(-1)=3f'(x)≤2Integrating w.r.t x;∫ f'(x) dx ≤ ∫2 dxf(x)≤2x+Cf(-1)=33=2(-1)+CC=3+2C=5

Q: Define g(4) for the given function so that it is continuous at x= 4. 5x - 80 g(x) = 5х - 20

A:

Q: Suppose f is a function that satisfies f(2) = 20 and f(2n) +nf(2) = f(2n + 2) for all positive…

A: It is given that, f(2)=20      ...(1) and  f(2n)+nf(2)=f(2n+2)     ...(2). Here, 'n' must be a…

Q: The function of f is increasing on I if ______ when x1 < x2.

A: We have to find when function is increasing

Q: Let h(x) = f(x)g(x). If f(x) = –3x² + 2x – 3 and g(x) = –3x² + 4x + 3, what is h' (1)? Do not…

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