What is the largest interval containing zero on which f(x) = sinx is one-to-one?

Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

A: To determine the critical values of a function, dfdx=0 Thus, differentiating f(x) w.r.t. x-…

Q: What are all absolute and relative extreme values of the function f(x)=– sin z on the interval (0,…

A: Given function f(x) - f(x) = -sinxDifferentiating on both sides with respect to x - f'(x) =…

Q: Explain why the function has at least one zero in the given interval.

A: Given function is  fx=x2-2-cosx over interval 0, π.

Q: Show that the function is continuous. f(x) = x sinx

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Q: Use the second order derivative test to find local exterma of the function  f(x) =x3-9x2-48x+72 on…

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Q: Describe the interval(s) on which the function is continuous. f(x) = sec x/4

A: The denominator can not be 0.

Q: Determine if the function f(x)= is continuous -- sin(x) x on the interval I= (0,1).

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Q: Find the intervals where the function f(x) = 2cosx + 1/ sin2x, 0≤x≤ 2π is concave up.

A: Let's solve.

Q: Find the open intervals on which the function is increasing or decreasing.

A: Given: fx=sinx-1, 0<x<2π To Find: Increasing and decreasing function.

Q: Find the intervals where the function 1 f(x) = 2cosx + sin2x, 0 ≤ x ≤ 2π is concave up.

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Q: Estimate the error in evaluating the function f(x)= e2x* sin x near the point x = 1.396, if the…

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Q: Is this a possible way to show that f(x) = arctan(2(x-1)) - lnIxI has exactly four real roots?

A: What is Rolle's Theorem: Rolle's theorem is the base of mean value theorem. More precisely, the mean…

Q: Find the absolute extrema of the function on the closed interval.                    f(x) = sin 2x,…

A: Approach: Without wasting any time, take the derivative of the original function. Find critical…

Q: Find the intervals of monotonicity of the function f(x)=x+sinx.

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Q: Find the open intervals on which the function is increasing or decreasing.     f(x) = sin x − 1, 0…

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Q: find the intervals on which f is increasing and decreasing. f(x)= sin^2x on [-pi,pi]

A: Given a function and interval,

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

A: Given function is fx=9-x2+sin-1x3.

Q: Explain why the function has at least one zero in the given interval. Function Interval f(x) = x2 -…

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Q: Q: Show that the function f(x)=- x sin ,X =0 is continuous at x = 0.

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Q: Find the absolute extremum f(x)=sinx    (30,120)

A: Given function is Differentiating with respect to x, we get Firstly, we find critical points of…

Q: Suppose f''(x) = -(sin(x)), f'(0)=6 and f(0)= -1 Find f(π/2) =?

A: Given query is to find the value of the function at indicated point.

Q: Find the intervals on which f(x) = cos2 x on [−π, π] is increasing and decreasing.

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Q: Show that the function is continuous on  (∞ , -∞).

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Q: Explain why the function ƒ(x) = sin (1/x) has no continuous extension to x = 0

A: Then we can extend the definition of the function at that point to make it continuous there.

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

A: Given: fx=tan-1xx2+2 we know that given functionfx is increasing, if f'x is greater than zero and…

Q: Find the domain of the function. f(x) = (6cosx)/(1 - sinx)

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Q: What are the intervals of monotonicity of f(x) = arctan (2(x-1)) - ln IxI ?

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Q: Consider the function f(x) = 1 - 7x² OI function on this interval, i.e. f(3)-f(-4) 2 4)

A: answer is in next step . please give a like !!

Q: A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f, the tangent…

A: Given problem:- A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f,…

Q: what is the value of x in second iteration of the function f(x) = sinx - X +5, in the interval of…

A: According to the fundamental theorem of algebra, every algebraic equation has a root. If the…

Q: 1) Verify the Mean Value Theorem for f(x)= x+sin(2x) over the interval [0, 2]

A: given f(x) = x + sin (2x)   defined over interval  [0, 2π]

Q: Find the intervals on which f is increasing and decreasing. f(x) = - cos 2x on [-1,1]

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Q: Show that the function has removable discontinuity at the origin sin 2x 2x f(x) = 1 if x = 0 if x =…

A: Given that a function f(x) and we show that the function has removable discontinuity at the origin .…

Q: Find the intervals of monotonicity of the function f(x)=1−sinxcosx.

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Q: Use the Intermediate Value Theorem to show that f(x) = 2+ sin r 3 tan x has a | (0. ). solution in…

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Q: Differentiate the function. f(x) = sin(x) In(3x) f '(x)

A: Here, you can use the product rule for derivative. ddx(u·v)=u·v'+v·u'

Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

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Q: Explain why the function has at least two zeros in the interval [1, 5].              f(x) = 2 cos x

A: To show the function has at least two zeros .

Q: identify open interval on which the function is increasing or decreasing. f(x)=sinx+2, 0<x<2pi

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Q: Find the inflection points for the function f (x) = 8x + 2 – sin (x) with 0<x< 3T. Express the…

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

Q: Find the open intervals where f is increasing or decreasing.ƒ(x) = -3 sin 4x

A: Given- fx=-3sin4x To find-  The open intervals where f is increasing or decreasing.

Q: What are the zeros of f(x) =8 sin x-4 on the interval [0,2r]?

A: We have to find the zeros of given function.

Q: 26. Show that the function has removable discontinuity at the origin sin 2x {²7, 2x 1 f(x) = if x =…

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Q: How many integers are there in the domain of the function f(x) = ln (x² – x – 12) + v25 – x² +…

A: The domain of a function is the set of input or argument values for which the function is real and…

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.