Expert: Paul Klarreich - 10/31/2006

Question
Find the slope of the graph of y=f(x) at the designated point.
f(x)=x^10+1+square root 1-x, (0,2)

Answer
Questioner:  brandon
Category:  Advanced Math
Private:  no
 
Subject:  differentiable calculus
Question:  Find the slope of the graph of y=f(x)

>> You are not supposed to say that.  You should be saying "the slope of THE TANGENT TO THE graph...".

at the designated point.
f(x)=x^10+1+square root 1-x, (0,2)
.............................
Hi, Brandon,

The slope of the tangent line is just the value of f'(x) at the given point.

If f(x) = x^10 + 1 + sqrt(1-x)   << note parenthesizing.

f(x) = x^10 + 1 + (1-x)^1/2
                   1
f'(x) = 10x^9 -  ----------
                2sqrt(1-x)  

Now try your  x=0:
               1
f'(0) = 0 -  -------
            2sqrt(1)

f'(0) = -1/2

That's it.