Find the linearization of f(x)=(1+x)^k at x=0. Your answer will be in terms of x and k.

Could you take a look at this one too when ya get the chance also @misty1212?

Specifically when I'm deriving (1+x)^k, would it equal k(1+x)^(k-1)?

Question

Find the linearization of f(x)=(1+x)^k at x=0. Your answer will be in terms of x and k.

Could you take a look at this one too when ya get the chance also @misty1212? 

Specifically when I'm deriving (1+x)^k, would it equal k(1+x)^(k-1)?

misty1212 · Answer

yes

misty1212 · Answer

course we didn't do so well with the last one, even though i am sure it was right

anonymous · Answer

No you were right it was asking for the formula, not the answer :(

anonymous · Answer

I didn't realize hahah

anonymous · Answer

Thanks for the help I really do appreciate it. I suck at this stuff.

misty1212 · Answer

$$\color\magenta\heartsuit$$

anonymous · Answer

I have

1^k+k(1+x)^(k-1)

But what would the (x-a) part equal of the equation? x=0, but what is a?

misty1212 · Answer

x is the variable, a is the zero

misty1212 · Answer

the point is $(0,1)$

misty1212 · Answer

you get 
$$f'(x)=k(1+x)^{k-1}$$ which at $x=0$ gives the slope of $k$

misty1212 · Answer

and the line of 
$$y-1=k(x-0)$$ or 
$$y=kx+1$$

anonymous · Answer

Got it! Thanks again

misty1212 · Answer

$$\color\magenta\heartsuit$$