Differentiation application

Question

analyze and sketch a graph of the following functions. Label any intercepts, relative extreme, points of inflection and asymptot.

f(x)=(x^2-1)(x^2-8)

Answer 1

f(x) = x⁴ -9x² +8  so f'(x) = 4x³ -18x =2x(2x²-9)  and f"(x) = 12x² -18.

 

This being a polyomial function, it has no asymptotes.

x-intercepts are {±1,±2√2} 

RELATIVE extrema occur when x = {0,±3/√2}

Inflection point occur when x = ±√(3/2).

You can rationalize denominators, etc, if you prefer, for these critical values and for x coordinates of inflection points.

 

Comprende?