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)#