SOLUTION: function: y= x^4-8x^3-16x+5
a. Identify the domain and range
b. determine the x and y-intercepts
c. determine the points of inflection with the second derivative test for the co
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Question 1180560: function: y= x^4-8x^3-16x+5
a. Identify the domain and range
b. determine the x and y-intercepts
c. determine the points of inflection with the second derivative test for the concavity
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
f(x)=x^4-8x^3-16x+5
f'(x)=4x^3-24x^2-16
f''(x)=12x^2-48x
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.
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.
c. points of inflection
The points of inflection are where the second derivative is zero.
The points of inflection are at x=0 and x=4.
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