Solution Found!
Graphing polynomials Sketch a graph of the
Chapter 7, Problem 13E(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.
\(f(x)=3 x^{4}+4 x^{3}-12 x^{2}\)
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.
\(f(x)=3 x^{4}+4 x^{3}-12 x^{2}\)
ANSWER:Solution: Step1 Given that f(x)=3*x^4+4*x^3-12*x^2 Differentiate the given equation to find f’(x) we get, f’(x)= 3*4*x^3+4*3*x^2-12*2*x = 12*x^3+12*x^2-24x Again differentiate f’(x) to find f’’(x) we get, f’’(x)=12*3*x^2+12*2*x-24 = 36*x^2+24*x-24 Step2 To get extreme values we have to use f’(x)=0 => 12*x^3+12*x^2-24x=0 =>12x(x^2+x-2)=0 => x(x^2+2x-x-2)=0 => x(x-1)(x+2)=0 Critical points are 0,1 and -2 Step3 To find inflection points we have to use f’’(x)=0 =>36*x^2+24*x-24=0 =>6(6*x^2+4x-4)=0 =>6*x^2+4