Graphing polynomials ?Sketch a graph of the following polynomials. identify local extrema, inflection points, and x?- ?and y-intercepts when they exist.

Solution: Step1 Given that f(x)=2*x^6-3*x^4 Differentiate the given equation to find f’(x) we get, f’(x)= 2*6*x^5-3*4*x^3 = 12*x^5-12*x^3 Again differentiate f’(x) to find f’’(x) we get, f’’(x)=12*5*x^4-12*3*x^2 = 60x^4-36*x^2 Step2 To get extreme values we have to use f’(x)=0 => 12*x^5-12*x^3=0 =>12x^3(x^2-1)=0 => 12x^3=0, (x^2-1)=0 => x=0, 1,-1 Critical points are 0,1 and -1 Step3 To find inflection points we have to use f’’(x)=0 =>60x^4-36*x^2=0 =>6x^2(10x^2-6)=0 =>10x^2-6=0 => 10x^2=6 =>x^2=6/10 => x=6/10 =>x=±0.7745 Evaluate f’’(x) at the critical points we get, f”(0 )=60x^4-36*x^2= 60*(0)^4-36*(0)^2 =0 at x=0 And f”(1)= 60x^4-36*x^2 = 60(1)^4-36*(1)^2 = 60-36=24>=0 Has a local minimum...