Solution Found!
Answer: Graphing polynomials Sketch a graph of the
Chapter 7, Problem 11E(choose chapter or problem)
9-14. Graphing polynomials Sketch a graph of the following polynomials. Identify local extrema, inflection points, and x- and y-intercepts when they exist.
\(f(x)=x^{4}-6 x^{2}\)
Questions & Answers
QUESTION:
9-14. Graphing polynomials Sketch a graph of the following polynomials. Identify local extrema, inflection points, and x- and y-intercepts when they exist.
\(f(x)=x^{4}-6 x^{2}\)
ANSWER:Solution: Step1 Given that f(x)=x^4-6x^2 Differentiate the given equation to find f’(x) we get, f’(x)= 4x^3-6*2x = 4x^3-12x Again differentiate f’(x) to find f’’(x) we get, f’’(x)=4*3x^2-12 = 12x^2-12 Step2 To get extreme values we have to use f’(x)=0 => 4x^3-12x=0 =>4x(x^2-3)=0 => 4x=0, (x^2-3)=0 => x=0, 3,- 3 Critical points are 0,- 3 and + 3 Step3 To find inflection points we have to use f’’(x)=0 =>12x^2-12=0 =&