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Numerical Analysis
- Find the minimum of the function f(x) = (X/log X) by using the quadratic-interpolation method with an initial trial step length as 0.1arrow_forwardConsider the function f(x) = -6x2 + 4x - 4. Find the critical point, A of the function. At x = A, does f(x) have a local min, or local max, or neither?arrow_forwardcalculate the average over the given interval. f (x) = x3, [0, 4]arrow_forward
- let f(x)=ex for 0 < x < 1 Approximate f(0.25) using linear interpolation with x0=0 and x1=0.5 . Approximate f(0.75) using linear interpolation with x0=0.5 and x1=1 Approximatef(0.25) and f(0.75) using quadratic interpolation with x0=0 and x1=0.5 and x2=1 Which is the better approximation??arrow_forwardConsider the function f(x)=−4x2+8x−3. f(x) has a critical point at x=A Find the value of A: A=At x=A, does f(x) have a local min, a local max, or neither? Type in your answer as LMIN, LMAX, or NEITHER.arrow_forwardFind the average value of the function on the given interval. ƒ(x) = x2 - 3; [0, 7]arrow_forward
- Compute the average rate of change of f(x) = x2 − 2x on the interval [1, 3]. Find c ∈ (1, 3) whichsatisfies the conclusion of the mean value theorem.arrow_forwardFind the average value of f(x) = x3e-2x over the interval [−1, 1].arrow_forwardFind the average value of the function f(x) =3x2-2x on the interval {1,4}arrow_forward
- Find the average value of f(x) = 1 / (4x2 − 1) from x = 1 to x = 4.arrow_forwardUse a graph below of f(x) = ln (3x^2 +1) to estimate the x-values of any critical points and inflection points of f(x).arrow_forwardFind the interpolating polynomial of the following point and function using Newton's interpolation process. y = ln ( x + 2 ) at x = [-1,2].arrow_forward
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