Question

Find the maximum and minimum value of the polynomial.12x^5 - 45x^4 - 20x ^3 +90x^2​

Answer 1

Answer:

answer for u r questions

Step-by-step explanation:







How do you find the inflection points off(x)=12x5+45x4−80x3+6?

Calculus  Determining Points of Inflection for a Function

1 Answer



MoominDave

Jun 22, 2018

Maximum: x=-4

Inflection: x=0

Minimum: x=1

Explanation:

In general, this is a hard problem for a quintic equation. But this particular quintic has some missing low order terms that help us a great deal.

To find the inflection and turning points of f(x), we follow the usual procedure and set f'(x)=0.

f(x)=12x5+45x4−80x3+6 so

f'(x)=60x4+180x3−240x2

Now this is a quartic equation. A full "solution by radicals" of the quartic is known, but it is long and complex (and painful to perform!). Fortunately, we can factorise this equation:

f'(x)=60x2(x2+3x−4)=60x2(x+4)(x−1).

So f'(x)=0⇒x=-4, 0, or 1.

To categorise these consider the second derivative:

f''(x)=240x3+540x2−480x=60x(4x2+9x−8)

f'