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- Find a function whose graph passes through the point (1,2/e) and satisfies x^2y'=y.Suppose that the first derivative of y = ƒ(x) is y' = 6(x + 1)(x - 2)2. At what points, if any, does the graph of ƒ have a local maximum, local minimum, or point of inflection?Suppose the derivative of the function y = f(x) is y' = (x-9)2(x+6). At what points, if any, does the graph of f have a local minimum or a local maximum?
- find a point c satisfying the conclusion of the MVT for the given function and interval y = x3, [−4, 5]Suppose the derivative of the function y=f(x) is y’=(x—1)^2(x—2). At what points, if any, does the graph of f have a local minimum, local maximum, or point of inflection?13. Find the minimum and maximum value of the function on the giveninterval.y = 2x 2 + 4x + 5 [-2, 2]
- find a linearization at a suitably chosen integer neara at which the given function and its derivative are easy to evaluate. ƒ(x) = x2 + 2x, a = 0.1Suppose g(-2)=3 and g'(-2)=-4. Let f(x) = x3 + g(x). Find the equation of the line tangent to y = f(x) at x = -2.Find a point c satisfying the conclusion of the MVT for the given function and interval. y = √x, [9, 25]