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- Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.Express the solution of the given IVP in terms of a convolution where g(t) is an arbitrary function.4. If the secant method is used on f(x) = x^5 +x^3 +3 and if x_(n-2) = 0 and x_(n-1) = 1, what is x_n?
- Suppose that the quadrature formula has degree of accuracy atleast 2 integral f(x)dx with upper limit 2 and lower limit -2 = a1f(−2) + a2f(0) + a3f(2) Use the definition of degree of accuracy to determine the constantsa1, a2, a3, and then determine the exact degree of accuracy of the quadratureformula. Is there any quadrature formula that has higher degree of accuracyand that also uses three functional evaluations?Suppose ff is differentiable on (-\infty,\infty)(−∞,∞), f(3)=12f(3)=12, and f'(3)=-2f′(3)=−2. Use linear approximation to estimate f(3.3)f(3.3)Calculate the M6 approximation for f(x) = 4(x + 18) on [5, 8]. M6 =
- Consider the following quadratic function: f(θ) = 1/2∑ni=1 wi(θ−xi)2, where x1,...,xn are points in 1D space taking on real values and w1,..,wn are positive real numbers denoting the importance of each of these points. What value of θ minimizes f(θ)?Which of the following is a critical point on the curve y = x3 − 3x2 + 4x + 5.Consider the cubic functionf (x) = ax3 + bx2 + cx + d, where a 0. Show that f canhave zero, one, or two critical numbers and give an exampleof each case.
- Suppose thatf(x)=x^3−6x^2+2.(A) Find all critical values of f. If there are no critical values, enter -1000. If there are more than one, enter them separated by commas. Critical value(s) =? (B) Use interval notation to indicate where f(x) is decreasing. Decreasing:? (C) Find the x-coordinates of all local maxima of f. If there are no local maxima, enter -1000. If there are more than one, enter them separated by commas. Local maxima at x =? (D) Find the x-coordinates of all local minima of f. If there are no local minima, enter -1000. If there are more than one, enter them separated by commas. Local minima at x =?3. Where is p(x) the worst approximation to r(x)? In other words, where is the vertical distance between the two functions maximized?Suppose there is no known formula for g(x) but we know that g (2) = - 1anc; g^ prime (x)= sqrt x^ 2 +5 for all x . Use a linear approximation to estimate g(2.1)