Given that f(x) =x-1 and g(x)=x-x, find (f+ g)(6), if it exists.

Q: What is the length L of the interval on which the function f(x)=x3−6x2−15x+8 is decreasing?

A: Given

Q: If f (x) = (e²)² , what is f'(x) ?

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Q: If f'(x) = 2x- x-2, then f has inflection point(s) with x – coordinate(s) equal to

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Q: Find the quotient x+h)-f(x) for f(x) = 7x – 3x²

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Q: Find f' (2) for f(x) = x²e2¤-3

A: To find the derivative of the given function we have to apply chain rule of differentiation and the…

Q: given f(x)=x4-8x2+2, find all x-values such that f(x) has horizontal tangent lines

A: Compute the derivative of the given function.

Q: Find the inflection point of the curve f(x)= x³ – 12x²+7x+1.

A: An inflection point is a point on the graph at which the second derivative is equal to zero or…

Q: If f(x) = (x² +2) e², what is f'(x)?

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Q: Find the critical points of the functionf (x) = 4x³ – 3x and the inflection point of the function…

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Q: Find a formula for f-'(x) and (f -1)'(x) if f(x) = V х-2

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Q: Given that f(x) =x+4 and g(x)=x -x, find (f+g)(1), if it exists. -X,

A: Given two functions f(x) and g(x). Then (f+g)(x)=f(x)+g(x)

Q: snip

A: Make the changes function in the  function (f+g)(x) by adding and subtracting terms such that…

Q: If f'(x) = x³ – 2x* + x³ + 2, then f has inflection points at

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Q: what is (f +g)(x) given that f(x) = 3x+4 and g(x) = 2x-5?

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Q: Find the critical point for the function f(x)=-x² +3x+1

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Q: If f(x)= 2x-and g(x)=3x+1, what is f(x)-g(x)+g(x)²? O8x6+9x2+3x O8x+9x-x O8x+9x2-3x O8x+9x+x

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Q: Given that f(x) = 3x – 1, g(x) = 2x and h(x) = x + 1, determine: a. hgf(x)  b. hgf(-2

A: Given : f(x) = 3x-1             g(x) = 2x             h(x) = x+1  To Find : hgf(x)…

Q: For the function f(x) = x³ – 27x, its local maximum is which occurs at ( its local minimum is which…

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Q: Find the value of a so that f(x)= x2 + a has a range of [-2, ∞).

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

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Q: Find the critical points of the function f(x)=8x3−x4.

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

A: Given: hx=fxgx, fx=4x2+3x+1, gx=3x2-3x-4

Q: Given that f(x) = 2x – 3  and h(x) =x2 - 4 Find:- i) f(-4) =   hᴏf(x)

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Q: Find f'(a) for x2 f(x) = x + 6 at a = 3.

A: Given function :

Q: Find the two x-intercepts of f(x) = x2 − 3x + 2 and show that f′(x) = 0 at some point between the…

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Q: By using (fixed point itration), Find a solution for f(x) = x3 + x - 1 = 0

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Q: If f(x)=5x-1, g(0)=2, g'(0)=4, and h(x)=f(g(x)), then what is h'(0)?

A: Given that h(x)=f(g(x)) Using chain rule we get: h'(x)= f'(g(x))g'(x) We plug x=0 So, h'(0)=…

Q: If f(x) = e2" , what is f"(x)?

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Q: 1. If f(x) = 2x – x² and g(x) = |x – 3|, find the value of f(-2) + g(-2)

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Q: If (f°g)(x)=2x-1,how might f(x) and g(x) be defined?

A: (f°g)(x)=2x-1 can be written as f(g(x)) So g(x) is the inner or the first function  And f(x) is…

Q: Determine all the critical points of the function f(x) = 3xe3*

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Q: Explain why g(x) = f(x), if x ≤2 0, if x > 2 is not differentiable at x = 2.

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Q: To find g(x + 1), what do you substitute for x in the function g(x) = 8x − 2?

A: To find g (x + 1).

Q: Find the Critical number of the function f(x) = -2x^2 + 16x + 7. x = ?

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Q: Given that f(x)= 5x+2 find f-1(x)

A: Given function is fx=5x+2. To find f-1x. Solution: Steps for finding inverse of the function. 1.…

Q: What is f (2) if the linearization of f (x) at a = 2 is L(x) = 2x + 4?

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Q: Find the critical numbers of the function.   f(x)  = x3 + 6x2 -15x

A: Critical numbers of a function are the values of x for which its first derivative is zero or…

Q: If f(x)= 2x²and g(x)=3x+1, what is f(x)+g(x)?

A: Solution is written in below steps.

Q: 7.If f(x)= 2x – 1 and g(x)= x² – 2x, find f(3)/g(2). -

A: Given fx=2x-1 and gx=x2-2x. To find: f3g2 Solution: Finding f3.  f3=2·3-1=6-1=5 Now, finding g2.…

Q: Given that f(x) = 7|x| + 3x  -1, Find: a) f(-x) b) -f(x) c) Is f(-x)= f(x)?

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Q: Find the critical points of the function f(x)=x2−4x+3x−2.

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Q: Find the inflexion point(s) of f(x) = x²-3x²³

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Q: What is the value of In[f'(2)]if f (x) = e*?

A: Our Aim is to tell the value of ln f'(2) if f(x)=ex-(i)

Q: Find the critical points of the function f(x) = 4x° – 12x.

A: The given function is fx=4x3-12x. The critical points of any function is given by f'x=0.

Q: Given that f(x) = 2x-2n + 8x², what value should be assigned to n to make f a function of degree 3?

A: Given f(x)=2x-2n+8x2. We need to find what value of n makes f(x) a function of degree 3.

Q: 4) Where is the function g(x) = 3x2 -x+ 5 differentiable?

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Q: Find the extreme values of the function f(x) = (x² + 2x)³ on the interval [-2, 1].

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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.