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Find the minimum value of the function f(x)=x^3−6*x^2+4x+12 in the interval [−2,6] within 10% of the exact value using the interval-halving method upto first iteration only.
3. Consider the function f(x) = 4x + 5 on the interval [-1.1]. (a) Find the quadratic Taylor approximation fr(x) = co + Cl2 + 22x2. Calculate the Ci to four decimal places. (b) Find the quadratic Legendre approximation fl(x) = do + 01x + 22x. Calculate the ai to four decimal places. If the two approximations differ greatly, something is probably wrong. You may want to consult section 4 in the pdf I sent you on orthogonal polynomials.
at the point (2, -3). Give an 4. Find the minimum value of the directional derivative of the function f(x, y)- exact answer. 2. at the point (2, -3). Give an 4. Find the minimum value of the directional derivative of the function f(x, y)- exact answer. 2.
Find the absolute maximum value and the absolute minimum value of the function f(x) = esin(x) on the interval [0,21]. Express the answer in terms of the natural number, e. Do not use decimal approximations of the answer. absolute maximum: absolute minimum:
For the function F(x) = find minimum value using two methods - a. Newton's method starting with initial point of 1 b. Golden section in the interval [0,2] required tolerance =0.001
can you please show hand calculations Find the minimum of the given function f(x) using the Golden Section Search at an interval 2,3.25]. Show hand calculated solutions, fill in the table, and use three decimals. Regarding MATLAB, plot the function and solve for the extremum using a built-in function. f(x) 3cos(a) sin(a) 2(2) 3.525 | -2:408|1o311 Find the minimum of the given function f(x) using the Golden Section Search at an interval 2,3.25]. Show hand calculated solutions, fill in the...
Given the function: f(x)=(x^2-4x+6)/(x-1)^2 a) Find the asymptotes of f, if any b) Find the first and the second derivatives of f c) Find the intervals of increase and decrease of f d) Find the relative maxima and the relative minima, if any e) Find the intervals where f is concave up and down, respectively, together with the points of inflection, if any.
1 Find the root of f(x) = x3-3 using the bisection method on the interval [1,2]. (Do three iterations). GatvEN ()5 1.5 (4) Cls .5).375 40 zor ( han R(1.25) 1.04675 1.2s fi.a) LS1-Ge1 1a5 1.25
Can you find a differentiable function f(x) defined on the interval [0, 3] such that , and for all x ∈ [0, 3]? Justify your answer (do not write only Yes or No, but explain your answer). We were unable to transcribe this imageWe were unable to transcribe this imagef'(x) <1
of 15 2 3 5 6 9 10 12 Suppose that the polynomial function f is defined as follows. s(x)-Sx (x+3)(x-6-8) List each zero of f according to its multiplicity in the categories below. If there is more than one answer for a mutiplicity, separate them with commas. If there is no answer click on Zero(s) of multiplicity one: Zero(s) of multiplicity two: Zero(s) of multiplicity three: