What are the points of inflection, if any, of $f(x)=4x^3+15x^2-150x+4$ ?

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Answer 1 · 2017-06-27T03:30:22

Inflection point is at $(-5/4, 1657/8) = (-1.25, 207.125)$

Given: $f(x) = 4x^3 + 15x^2 - 150x + 4$

Points of inflection are found when $f''(x) = 0$ . First find the first derivative:

$f'(x) = 12x^2 + 30x - 150$

Find the second derivative: $f''(x) = 24x + 30$

Find inflections, $f''(x) = 0$ :

$24x = -30$

$x = -30/24 = -5/4$

$f(-5/4) = 4(-5/4)^3 + 15(-5/4)^2 - 150(-5/4) + 4$

$= 1657/8 = 207.125$

Inflection point is at $(-5/4, 1657/8) = (-1.25, 207.125)$

What are the points of inflection, if any, of f(x)=4x^3+15x^2-150x+4 f(x)=4x^3+15x^2-150x+4 ?