math ppl please help!!!!!! i dont understand how to do this n i need the extra credit!!!!!?

Question

Let f(x)=x^5+2x^3-2

a) show that f has exactly one zero
b) use the Intermediate Value Theorem to locate the interval where the zero lies in
c) use Newton's method to approximate the zero to 5 decimal place accuracy

Answer 1

The derivative is 5x^4+6x^2 >= 0 It is 0 at x= 0 but doesn´t change sign so the function is always increasing.
Its limit at x=>- infiniy is - infinity and at + infinity its limit is + infinity.
So there is onñy one root
At 0 f(0)=-2 and At 1 f(1) = 5>0 The root lies between 0 and 1
Newton' method is routine work.I leave it to you

Answer 2

that = x^3(x^2+2x-2)=x^3(....................