28 Jun, 2021 02:01 PM

maxima/minima/inflection points of: y= ax^3 +bx^2 +cx + d?

Assuming a,b,c,d>0 and that they have maxima/minima and inflection points, find the x and y coordinates of the maxima/minima and points of inflection

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ST
28 Jun, 2021 02:01 PM

You know how to differentiate, right? Just do it like you'd do any other "find the maxima" question, except that your answer will be in terms of a, b, c and d.

HU
28 Jun, 2021 02:01 PM

all of us comprehend that: f(a million) = 0 f(2) = 9 Differentiating, we get: f'(a million) = 3 f'(2) = 18 So, we've the equipment: A + B + C + D = 0 8A + 4B + 2C + D = 9 3A + 2B + C = 3 12A + 4B + C = 18 fixing, we get: A = 3 B = -6 C = 6 D = -3 which aspects us the polynomial function: ? f(x) = 3x³ - 6x² + 6x - 3 for which: f(a million) = 0 f(2) = 9