Saturday

July 26, 2014

July 26, 2014

Posted by **Claire** on Thursday, July 5, 2012 at 2:44pm.

Formal definition of a derivative?

or slope between two points?

- math -
**Steve**, Thursday, July 5, 2012 at 3:34pmthe slope at a point a is the slope of the line tangent to the curve at x=a.

To get that, pick a point number b, near a, and think of the slope between two points on the curve at f(a) and f(b).

As b gets closer and closer to a, the line between the two points gets closer and closer to the tangent line.

Finally, when b=a, the two points are the same point, and the line is tangent to the curve.

That's all the formal definition of the derivative is. It's the limit of the slope of a line joining two points on the curve, as the two points get closer and closer to each other.

**Related Questions**

calculus - f(x)=1/x^2 use formal definition of derivative to find slope at x=2

12th Grade Calculus - 1. a.) Find an equation for the line perpendicular to the ...

calculus - 1. Given the curve a. Find an expression for the slope of the curve ...

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

Calculus - The line that is normal to the curve x^2=2xy-3y^2=0 at(1,1) ...

Math - How can I determine a value of gradient from a graph if the line is ...

crt - To introduce an unusual or unfamiliar word, to coin new words, or to ...

calculus - Find the equation of the tangent line to the curve y=sqrt(x) at x = c...

physics - I'm making a graph of force vs stretch for springs. I have 7 data ...

algebra - Find the slope of the line through the given points. (2,4) (6,-3). m=...