Polynomials and Induction help (1 Viewer)

[yeezus]

I need help with these 2 questions, one is on polynomial and the other is induction.

1. A polynomial is given by f(x)=(x-7)^2 Q(x). Show f(-1) =f'(-1)=0

2. Prove by induction -4 + 8 - 16 +...+4(-2)^(n-1) = [4(-2)^n -1]/3 for all n>or equal to 1

Cheers,

 

[Carrotsticks]

Did you use the Product Rule to differentiate #1?

 

[yeezus]

does it become f'(x) = (x+1)^5 g'(x) + g(x) 5(x+1)^4

 

[braintic]

Not sure how (x-7)^2 becomes (x+1)^5 . The question as it stands is wrong.

 

[anomalousdecay]

I need help with these 2 questions, one is on polynomial and the other is induction.

1. A polynomial is given by f(x)=(x-7)^2 Q(x). Show f(-1) =f'(-1)=0

2. Prove by induction -4 + 8 - 16 +...+4(-2)^(n-1) = [4(-2)^n -1]/3 for all n>or equal to 1

Cheers,

1.










I don't think either of your questions are right, but I did 1 for the sake of it.