Question

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Your answer is incorrect. Try again. Use the derivative to find the critical pomt of f(a) Az2 B C Assume thar A B, and C are nonzero constaats a t Click if you would like to Show Work for this question: Open Shos Work

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Answer 1

Given that f (x) = Ax^2 + Bx + c Differentiating with respect to x we get f^' (x) = 2A x + B Now f^' (x) = 0 Thatimplies 2Ax + B = 0 Thatimplies 2Ax = -B Thatimplies x = -B/2A (since A is non zeo) Therefore f (-B/2A) = A . (-B/2A)^2 + B . -B/2A + C Therefore f (-B/2A) = A . (-B/2A) + B . -B/2A + C = B^2/2A - B^2/2A + C = 0 Hence correspond to x = -B/2A we get the critical point and the point is (-B/2A, C) 2) Given that f (x) = A x^3 - Bx Differentiating with respect to x we get f^' (x) = 3A x^2 - B Now f^' (x) = 0 Thatimplies 3Ax^2 - B = 0 Thatimplies 3Ax^2 = B Thatimplies x^2 = B/3A (since A is positive) Thatimplies x = plusminus squareroot B/3A Therefore Left most critical point at