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- Find the first and second derivative of any function defined implicitly by yx2+ y2= xCompute the second derivative of f(x)=ex+x at x = 1 using a step size h = 0.2Suppose that the first derivative of y = ƒ(x) is y'= 6x(x + 1)(x - 2). At what points, if any, does the graph of ƒ have a local maximum, local minimum, or point of inflection?
- 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?If ƒ(x) = xn, n ≥ 1, show from the definition of the derivative that ƒ'(0) = 0.Find the equation of the tangent line to the graph of f(x) = 4^(x/ln2) at the point where x is ln16.
- If the instantaneous rate of change of ƒ(x) with respect to x is positive when x = 1, is ƒ increasing or decreasing there?show derivatives of : a. y = ex^3+5x3 b. y = ln(2x4+2)3What 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?