:) If you are approximating the function f(x) = e¯ª on the interval |0, 1] by a piecewise cubic function and the desired error is less than 1 x 10-4, how many intervals do you need to divide [0, 1] into?

Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 20 over the interval [1, 3]. [2 - marks]

A: We have to find the absolute extremum values of the given function.

Q: Find the critical numbers of the function. f(x) = x² log,(x? + 2)

A: fx=x2log7x2+2⇒fx=x2logx2+2ln7      ∵logab=logblna Critical numbers are the values of x for which…

Q: f f(x) = ln(x2+10x+16) ov

A: The absolute minimum of f(x) is 6ln(2) and the absolute maximum of f(x) is 4ln(2)

Q: Suppose there is no known formula for g(x) but we know that g (2) = - 1anc; g^ prime (x)= sqrt x^ 2…

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Q: 3. Consider the function f(x) = e" on (0, 2), and a point a e (0, 2]. Consider the triangle formed…

A: Given function f(x)=e-x on [0,2]. The objective is to find the point a such that the triangle has…

Q: Given f(x) = 2æ – 33x2 + 168x + 7 over the interval of 0 < x < 10 , answer the following: a) The…

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Q: 3) Given the function f (x) = x – Cos x Using the bisection method in the interval (0, "), find the…

A: Given function is fx=x-cosx initial guess:- x0=0,   x1=π2 True value xr = 0.7391 (by graphically)

Q: 38 Find the critical numbers of the function. 25. f(x) = x³ + 3x² – 24x %3D -

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Q: Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ≈ T₁(x) when x lies in…

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Q: 1. Consider finding the root of f(x) =x´ – 5 use secant method, ɛ = 0, and start with the a interval…

A: given , f(x) =x2 - 5  we have to find roots of f(x) in interval by using secant method

Q: 1) Find the absolute extremum values of f(x) = x² [1, 2]. – 2x + 12 over the interval

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Q: Given that f(x) = -x +12x – 34 has a relative maximum at x = a. f' is negative on the interval (-…

A: Given query is to find the correct option for the f(x).

Q: 3. Iff has a local maximum at x – 1, then what can you say about f'(1)? What if you also know that f…

A: Given: The function fx has a local maximum at x=1. First derivative test: Let f be differentiable…

Q: 2. Find the extrema of the function g(x) = x3 using any of the methods given in the above…

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Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 12 over the interval [1, 3].

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Q: Bisection method was used to determine a root for a function f(x), using initial interval (x1, xµ)…

A: Consider the given information. Let the Initial interval be (xl, xu) Then h=xl-xu Which is the…

Q: On the graph of f(x) = cos x and the interval [-2n, 0), for what value of x does f(x) achieve a…

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Q: 2. Find the absolute maximum and minimum values of f(x)= x³ – 3x +1 over the interval [0, 3].

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Q: If f(x)= (x^4) + 3x + 1 and there are two roots x=a and x=b in the interval [-3,-1] with a &lt;b.…

A: The given function is,

Q: 7) Find the absolute maximum of the function f on (0,E) S(x)= 10xe

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Q: Find the absolute maximum and minimum values on the interval: g(x) = Vx(8 – x), [0,8]

A: our objective is to find the absolut maximum.

Q: Find the absolute minimum of the function f(x)= = 02 GW/N 0.3 4 O 1 0-2 01 2 2x x2 +4 on the…

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Q: 4. If f has a local minimum at x = 0 and a local maximum at x – 2, what can you say about f'(0) and…

A: f has a local minimum at x=0 and a local maximum at x=2.

Q: 3. The function f(x) = x^4 − 4x^3 + 8x has a critical point at x = 1.(a)  Find f"(x).   (b) Then use…

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Q: 1 5. By using the cubic approximation of f(x) = --1 around a = 0 in question 4, estimate the error…

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Q: for what value of x does the function f(x)=x^3-3x^2 attain absolute maximum in the internval (-1,4)

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Q: If f has a local minimum at x = 0 and a local maximum at x = 2, what can you say about f'(0) and…

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Q: On the graph of f(x) = sin x and the interval [27, 47), for what value of x does f(x) achieve a…

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Q: 2 The reliability of a turbine blade is given by R(t) = to, where to is the maximum life of the…

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Q: Find the absolute maximum and minimum values of the function g(x) = 2x− 4sin(x) on the interval [0,…

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Q: If b > 3 and average value of f(x) = 6x – x² on the interval [0,b] is 6, then what is b equal to?

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Q: Find the critical numbers of the function f(x) = 14x + |x|. In the answer boxes below, enter the…

A: Given: f(x)=14x3+|x| Definition: Critical points are the points where the derivative of function is…

Q: if x1 O No, since g(x) is undefined at x=1. O Yes, and g'(1)=3. O Yes, and g'(1)=8. O No, since g(x)…

A: Given

Q: 1) Find the absolute extremum values of f(x) = x2 – 4x + 18 over the interval [1, 4]. [2 marks]

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Q: Find the critical points of the function h(x) = 3x – 4r³ – 72a + 5 Enter your answers from smallest…

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Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 10 over the interval [1, 3].

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Q: Find the absolute maximum and minimum values of f(x) = (x² + x)i over the interval [-3, 4]. absolute…

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Q: Find the absolute maximum and absolute minimum values of f(x) = 3x^4 +4x^3 −12x^2 +1 on the given…

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Q: If f(x) = x2+1 for x > or equal to 0, then is arcf(x) has a tangent at x=1

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Q: Find the exact solution of the function via calculator, then find the numerical solution by using…

A: Given function is fx=2-ex2+x boundaries 0≤x≤1 and h =110       h =0.1   (1) Exact solution:…

Q: 2. The function (x) = x² is differentiable at x = 1. Find the function & such that o(x) = o(1) +…

A: Introduction: A technique for determining a function's derivative is differentiation. Mathematicians…

Q: Find the critical numbers of the function f(x) = 9x3 + |x³ – x²|. In answer boxes below, enter the…

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Q: Consider the region bounded above by g(x)=−9x−9 and below by f(x)=x2 −9x−18. Find the area, in…

A: Calculation:The given curves are f(x) = – 9 x – 9 and g(x) = x2 – 9x – 18.The area enclosed by two…

Q: What is the x-coordinate of the global minimum of the function f(x) = x – 3 ln x – 2 for the…

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Q: 3. Consider the function f(x) = r - 1+x 1- a. Explain why, when evaluated in a floating point…

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Q: 1) Find the absolute extremum values of f(x) = x² – 4x + 8 over the interval [1, 4].

A: f(x) = x2 – 4x + 8

Q: If f(x) = x² + k find k so that f has a critical number at x = 3. %3D

A: To find the critical number for any function fx we have to solve the derivative f'x=0. That is we…