Sunday

December 21, 2014

December 21, 2014

Posted by **help needed** on Friday, July 6, 2012 at 3:17pm.

use formal definition of derivative to find slope at x=2

- calculus -
**Steve**, Friday, July 6, 2012 at 3:48pmf'(x) = lim(h->0) [1/(x+h)^2 - 1/x^2]/h

ignoring the limit notation for now, we have

(x^2 - (x+h)^2)/(hx^2(x+h)^2)

= (-2hx-h^2)/(hx^2(x+h)^2)

= -2(x+h)/(x^2(x+h)^2)

= -2/(x^2(x+h))

lim(h->0) is thus -2/x^3

at x=2, that's f'(2) = -1/4

**Answer this Question**

**Related Questions**

math - What is the definition of the slope of a curve at a point x=a? Formal ...

Calculus 1 - Could you please explain how to find the slope using the definition...

calculus - Find the derivative of the function using the definition of ...

Calculus - If f(x) = 2 √x, use the definition of derivative to find f&#...

Calculus - (1 pt) If f(x) = 2 √x, use the definition of derivative to find...

Calculus derivative - find the slope m and an equation of the tangent line to ...

Calculus derivatives - f(a) = a + √a (a) Find the derivative of the ...

Calculus - Find the derivative of the function using the definition of a ...

Calculus - Find the derivative of m(x)=1/(x+1) by using the definition of the ...

Calculus - show that the curves r=asin(è) and r=acos(è) intersect at right ...