heartshapes
New member
- Joined
- Feb 21, 2008
- Messages
- 36
Alice and Bob are excited. They rush into your room and announce they have come up with their very own definition of derivative. Here is their formula to calculate the derivative of of a function f.
lim f(x+h)-f(x-h)/2(h)
h->0
a) draw a graph that demonstrates how their difference quotient formula relates to slope of a secant line and why (at first) it appears reasonable for finding the slope of a tangent line to y=f(x) at the point (x,f(x))
b_ Uh, oh bad news. Explain how Alice and Bob have overlooked a serious problem with their alternative definition of derivative. Hint: Find an example of a function where there is no well defined tangent line slop at point (x,f(x)) but Alice and Bob's definition would produce a limit that gives a definite value.
lim f(x+h)-f(x-h)/2(h)
h->0
a) draw a graph that demonstrates how their difference quotient formula relates to slope of a secant line and why (at first) it appears reasonable for finding the slope of a tangent line to y=f(x) at the point (x,f(x))
b_ Uh, oh bad news. Explain how Alice and Bob have overlooked a serious problem with their alternative definition of derivative. Hint: Find an example of a function where there is no well defined tangent line slop at point (x,f(x)) but Alice and Bob's definition would produce a limit that gives a definite value.
