1. AP Calculus Warm up 9.14.18
What is the derivative of a function?
The derivative of a function is also a
function which gives us the instantaneous
rate of change (or slope) of the curve at
any given point.
2. The Lame Joke of the day..
And now it’s time for..
What did one shooting star say to the other?
Pleased to meteor.
3. AP Calculus Warm up 9.14.18
What is the derivative of a function?
The derivative of a function is also a
function which gives us the instantaneous
rate of change (or slope) of the curve at
any given point.
12. What is the equation of the tangent
line of f(x) at ( 2, 12)
2
3)( xxf
Slope = 12
13. Time (t)
minutes
0 2 9 20 35
Temperature
C (t) in
degrees
Celsius
60 63 89 102 110
A beaker is being heated continuously over time (t) and is modeled by the
twice differentiable function C (t). The table above gives selected values of
the temperature in degrees Celsius. Estimate the instantaneous rate of
change of the temperature at 14 minutes. Indicate units of measure.
14. What makes a function
differentiable?
1. It MUST be continuous.
2. The derivative from the left must equal the
derivative from the right.
15. Most common times when a
derivative does not exist.
1. At a sharp corner 2. At a vertical tangent line
or asymptote