Expert: Paul Klarreich - 1/23/2006

Question
Hi Paul,

Wondering if you can help me with a review problem that I'm having trouble with? It is in regard to differentiation. Thanks for your help!!



Compute the derivative of the given function and find the slope of the line that is tangent to its graph for the specified value of the independent variable.

f(x)=1/x^2; x=2

Answer
Hi, Carson,

Your question:

Compute the derivative of the given function and find the slope of the line that is tangent to its graph for the specified value of the independent variable.

f(x)=1/x^2; x=2

There is more than one way to do this.  I will give you one, BUT IT MIGHT BE WRONG FOR THE CONTEXT OF YOUR REVIEW.  You will have to judge.  (Judge from the nature of the other problems around it.)

STANDARD WARNING: THE MATERIAL BELOW MAY CONTAIN FRACTIONS AND OTHER MATERIAL INAPPROPRIATE FOR CERTAIN COMPUTING SYSTEMS.  BE SURE TO VIEW IT IN A FIXED-SIZE FONT, SUCH AS COURIER.


You want f'(2), i.e. the value of the derivative at x = 2.

f(x) = 1/x^2 = x^(-2)
                   -2    
f'(x) = -2x^(-3) = -----
                   x^3

        -2      -2     -1
f'(2) = ----- = ---- = ----
        2^3      8      4

Did you know that the derivative of x^n is  nx^(n-1)?  If not, then this was the wrong way to do it.  In that case, let me know.