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- Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.When the Second Derivative Test Fails Analyze the critical points off (x, y) = 3xy 2 - x 3 .To determine maximums and minimums by the Second Derivative Test, we differentiate y"=72 / (2-8)3 Substituting x = 14 into y'', _____ <,>, 0r = Substituting x = 2 into y'', ______ <,>, or =
- Encounter the critical points of f(x, y) = 16x3 - 9y2 - 36x2 - 12y + 6x - 27 and then denote each point's nature with the second derivative test.Use the first derivatives test to find local exterma of f( x) =x3 -12x on RWhat is the numerical approximation of the derivative of the function f(x) = x^3 - 2x + 1 at x = 2 using the forward difference formula with a step size of h = 0.1?
- If ƒ(x) = xn, n ≥ 1, show from the definition of the derivative that ƒ'(0) = 0.What is the approximate value of the derivative of the function f(x) = 2x^3 - 5x^2 + 3x at x = 1, using a forward difference approximation with a step size of h = 0.1?What is the value of the first order derivative of the closed function given as x3+y3+3xy+3y2+6x+6y=0 at the point x = 1 ?