If f(x)=x-8x+12. Find the intervals on which f(x) is increasing or is decreasing- O a. Increasing on the interval (- 00, 4] Decreasing on the interval [4, 00) b. Increasing on the interval [-4, 00) Decreasing on the interval (-8-4] Oc. Increasing on the interval (- 00, -4] Decreasing on the interval [-4, o0) O d. Increasing on the interval [4, 00) Decreasing on the interval (-00,4]

Q: 2 2 x >1 4 2x> 2 4 x+ 2 b) f(x) = . 16 52x>4 x² + b 6 2 x > 5 1)is the above function continues at…

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Q: Where is the interval increasing and decreasing. Which interval or union of intervals represents the…

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Q: -10 f(x) = -8 -6 Equation, inequality, interval notation 2x - 3, x<-2, [-2,3) 8 1 113 x + 4, -2 1…

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Q: The intervals of increasing and decreasing for the function f(x) = (x – 4)² + 8 is increasing in [6,…

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Q: #9: Suppose you have a function f (x) that has x intercepts as -3, 1, and 5. If f(0) = -20, what can…

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Q: x2 - 8 If f(x) = X-4 where is f not differentiable?

A: Find where is f not differentiable

Q: - 2< x< -1 f(x) = {-2 -1< x< 1 .0 1< x< 2

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Q: Find the average rate of change of f(x)=7x^2-5 on the interval [2,t]. Answer with an expression

A: Use formula of avg rate of change

Q: 2 > x>1 4 2x > 2 52x>4 62x>5 (4 x + 2 b) f(x) = 16 x² + b 1)is the above function continues at x=2.…

A: We use the definition of continuity at a point to solve the given question, i.e., A function f(x) is…

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Q: For the function f(x) - 12x +11, find all intervals where the function is increasing: f is…

A: Given the function f(x)=x3−12x+11

Q: If the function f is increasing on the intervals (-5,1) and (9,21) and decreasing on the interval…

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Q: Given the function f (x) = 3x25 – 6x24. Determine the intervals for which the function - is…

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Q: (x-1 f(x)= {2x -1 |-3x +8 if if xs-2 if -2 4 f(-1) = f(-4) = f (5) =

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Q: Find the net change in the value of the function between the given inputs. f(x) = 8 − 3x;    from 4…

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Q: The function f(x) 1-7 is 94z2 Select one a. Increasing on (-1, 1) and decreasing elsewhere. O b.…

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Q: Find the open intervals on which the function is increasing or decreasing. (Enter your answers using…

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Q: from the function f(x) = 3x4 − 4x3 − 12x2 + 5 Find the absolute extreme values of f on the closed…

A: To find out extreme values of f(x) i.e. maximum and minimum values, first we need to calculate…

Q: A friend looks at the graph of y3x and observes that if you start at the origin, the graph increases…

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Q: Evaluate the piecewise defined function at the indicated values.

A: fx=x2+2x        if x≤-1x                  if -1&lt;x≤1-1               if x&gt;1

Q: If f(x) is an even function defined on the interval [-5,5], Then find - X+1 the real values of x…

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Q: x² – 3x – 2 - if r<-1 x – 1 x + 3 f(x) = if - 1<x < 1

A: limx→-1-f(x)=limx→-1-x2-3x-2x-1=(-1)2-3(-1)-2-1-1=1+3-2-2=-22=-1

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Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = 12 +…

A: Given: fx=12+x-x2 we know that for any function it is increasing then f'x has to be greater than…

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Q: 9) Solve for f '(x) given f(x)= 2*

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Q: 4. Find the absolute extreme values of f (x) = x²/3 (4 – x²) on the interval [-2, 2].

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Q: During a flu epidemic, the total number of students on a state university campus who had contracted…

A: "Hey, since there are multiple subparts posted, we will answer first three subparts. If you want any…

Q: Determine the value of the constant a for which the function f(x) is continuous at - 3. x2 +8x + 15…

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Q: ind the intervals where f(x)= x3-2x2+8 is increasing and the intervals where it is decreasing

A: Given query is to find the interval where f(x) is increasing and decreasing.

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) =…

A: we have to find the intervals on which f(x) is increasing and the intervals on which f(x) is…

Q: 1 - f 1 = f + - Solve - for f.

A: We have to solve the equation for f: 1s=f+1-fp Taking LCM in RHS side, we get 1s=f+1-fp1s=pf+1-fp…

Q: х - 2, for xS -3, f(x) = - 3, for - 3<x<1, 4х, for x2 1

A: Given,

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing.

A: Given, f(x)=-x44+x3-x2 we have to find the intervals on which f is increasing and the interval on…

Q: For what intervals is f(x) = x* – 8z² +3 decreasing? O The graph is decreasing on the interval (0,…

A: givenf(x)=x4-8x2+3f'(x)=4x3-16xf'(x)=4x(x2-4)so critical points will be -2,0 and 2

Q: if x<1 If f(x) = solve for a if f(-2) = f(4). -x+a if x 21

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Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x4 -…

A: Increasing and decreasing functions: f(x)=x4-4x3+4x2 Increasing function Let y=f(x) be a…

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Q: Find the intervals on which ƒ is increasing and the intervals on which it is decreasing. ƒ(x) = 4 -…

A: Given, fx=4-x2

Q: The intervals of increasing and decreasing for the function f(x) = (x – 4)² + 8 is increasing in [5,…

A: The given function is: f(x)=(x-4)2+8

Q: Determine the value of the constant a for which the function f(x) is continuous at - 3. x2 + 8x + 15…

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Q: Determine where the given function is increasing and where it is decreasing. 6) f(x) = 45x3 – 3x5 A)…

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Q: the intervals where the function is increasing and the interval is decreasing  f(x) = 1/3x^3 - 5x^2…

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Q: f(x)=x3-27x on [-4,4] absolute Min Absolute Max

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Q: Find the approximate root of the function f(x) = x^3 - x - 9 in the interval [-3,3] for 2 iterations…

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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.