Question 1180560
<br>
{{{graph(400,400,-2,10,-800,200,x^4-8x^3-16x+5)}}}<br>
f(x)=x^4-8x^3-16x+5<br>
f'(x)=4x^3-24x^2-16<br>
f''(x)=12x^2-48x<br>
a. domain and range
The function is a polynomial; the domain is all real numbers.
The function is a polynomial of even degree with positive leading coefficient; it has a minimum value but no maximum.  Find the minimum value using a graphing calculator.<br>
b. x- and y-intercepts
The x-intercepts are where the function value is zero.  Use a graphing calculator.
The y-intercept is where x is zero.  Trivially, f(0)=5.<br>
c. points of inflection
The points of inflection are where the second derivative is zero.
{{{12x^2-48x=0}}}
{{{12(x)(x-4)=0}}}
The points of inflection are at x=0 and x=4.<br>