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

Algebra ->  Radicals -> 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      Log On


   

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) About Me  (Show Source):
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graph%28400%2C400%2C-2%2C10%2C-800%2C200%2Cx%5E4-8x%5E3-16x%2B5%29

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.
12x%5E2-48x=0
12%28x%29%28x-4%29=0
The points of inflection are at x=0 and x=4.