1. Find the exact' maximum value and exact minimum value of the function on the given interval. Explain your reasoning using calculus. (a) z(t) = for t in [0, 12] (b) g(x) = sin(x) – cos(x) for æ in [-14, 12].

Q: 20. Sketch the function with the following properties: f'(x) 0 on (-2,0) f"(x) 0 on (-co, -1)…

A: From the given information, following results can be deduced.

Q: Find constants a and b in the function f(x) = axe“ such that fE) = 1 and the function has a local…

A: The given function is fx=axebx. It is given that f15=1. So, f15=a·15·eb·151=aeb55aeb5=5

Q: 2. Ali is seated on the line which is normal to the curve f(x) = x² - 2x + 4 at the point (1, 3). 3.…

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A: In this question we have to find the absolute maximum and absolute minimum.

Q: 4. Determine the constants a, b, and c so that the curve defined by f (x) = ax³ + bx² + c will have…

A:

Q: 4. Determine the maximum point of the the graph of y = 12 sin(π – 2x), for x = [-T, T).

A: Given:         y=1-2sinπ-2x     To get the maximum value of the function the derivative is equal…

Q: If f(x)= 2- cos(x) sin(x) then the absolute minimum of f on the 3T interval | 프,프15: 4 O 2/2-1 O…

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Q: Find the Wronskian for the set of functions.{e3x, sin 2x}

A:

Q: 6) Suppose f (x) is a differentiable function such that f (1) = 7 and f'(1) = 2. Use a tangent line…

A: This question is based on deduction of straight line using given information.

Q: Which of the following functions of x is guaranteed by the Extreme Value Theorem to have an absolute…

A: Option (C) is correct. Because the given function is continuous in the interval [0 4].

Q: 11. Find the linear approximation to given function at indicated point (Баллов: 2) x2 z = 3 + +, Po…

A: Topic:- linear approximation

Q: 4 Given that f(2) is analytic at z = 0 and that f G) =, n = 1,2, 3..,find f(2). VE

A:

Q: (1) Let f(r, y) = (x + y)e-=v. a) Determine the quadratic approximation function of f(r, y) at the…

A:

Q: 1. Discuss the continuity and differentiability of the function g(t) at t = 1, where t3, t 1.

A: Given that : g(t)= t3,  t≤1t  ,  t>1.  Let us check the continuity at t=1 :…

Q: Find the maximum and minimum values of the function f(x) = x – sin x on [0, 27). %3D

A: The given function is: f(x)=x-sinx For maximum and minimum value, differentiate the function and…

Q: The slope of the tangent line to the graph of the function y=3V-4at (16,8) is 16.00 4. -1.00 O-0.50…

A: Now,

Q: 1. Suppose that f(x) = -ar/2 + bæ/2. Reparameterize this function in terms of the location of the…

A: given fx=-ax32+bx12 differentiate the function with respect to x f'x=-32ax32-1+12bx12-1…

Q: 5. Find the exact absolute maximum and absolute minimum values for f(x) cos(x) + sin (x) on the…

A:

Q: 4 ース -where do es t have relahive minimums ? the relahi ve minimum is which occuRs at X= where does…

A: topic- relative maximum and minimum of function  relative minimum is the value of function where…

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A: We need to find the first two intervals of on the interval

Q: 9. Show the function f(z) = 1 + 2i+2Re(z) is differentiable or not differentiable at any points.

A: Solution

Q: 19.D. Show that the function defined by g(x) g² sin (1/x), x * 0, %3D = 0, 0, is differentiable for…

A:

Q: 1. Employ the following methods to find the maximum of f(x) = 4x – 1.8x² + 1.2x – 0.3x* (a)…

A: Given f(x)=4x-1.8x2+1.2x3-0.3x4. To find: (a) find the maximum using golden search method.…

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A: Topic:- application of derivatives

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Q: 2.4 Use the definition of the derivative of complex function to show that f(z) is not dif-…

A: The Complex Derivative Definition: Let f be a function defined on a neighborhood of z0 ∈ ℂ. If…

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Q: Answer the following questions about the functions whose derivativesare given:a. What are the…

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Q: 25. Use the definition of differentiability to prove that the following function is differentiable…

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Q: Suppose that f is a differentiable function with f(2) = 5 and f'(2) = 7. Let h(x) = f(e*). Find an…

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Q: 2 4. Find the most general analytic function f(z) of the variable z = x+iy whose imaginary part is…

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A: To analyze the critical point (0,pi/4) of the given function of two variables

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Q: The Second Derivative Test cannot be used to conclude that x = 2 is the location of a relative…

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Q: Find the global minimum of the function f (x) 1 + x² on the interval (0, co0)

A: Given that f(x)= 1+x2.  And we find global minima on the interval (0, infinity).     Here i attached…

Q: 2. For which of the following functions and domains does the Extreme Value Theorem guarantee the…

A: The Extreme value theorem states that if a function is continuous on a closed interval [a,b], then…

Q: 7. Find the c value(s) that satisfy Rolle's Theorem for the function f (x) = x* – 4x² on the…

A:

Q: 7. Suppose that the function f (x)=2-sin(e*) is continuous on with equal step 2'2 size, h equal to .…

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Q: 1o9.. 10 11 12 What is the minimum value of y = -3 – 5 sin (4x)?

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Q: 7. Find all values of x on the graph of f(x)=(x-1)´(2x+1) at which the tangent line is horizontal.…

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Q: 15. Find any local maximum and local minimum values , then sketch each curve by using first…

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Q: If f(x)= 2- cos(x) sin(x) , then the absolute minimum of f on the 3T is: interval O 13 O 0 P 2/2-1 O…

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Q: Suppose f is a function such that f(z) = 4z' and f" (z) = 12z. Which of the following is TRUE? f has…

A: Suppose f is a function such that f'(x)=4x3  &  f"(x)=12x2

Q: 2. For which of the following functions and domains does the Extreme Value Theorem guarantee the…

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: