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Introduction to Calculus: Differentiation - Coggle Diagram
Introduction to Calculus: Differentiation
Real-life problem: minimise the cost of standard soda cans production
define variables
define measurement units
Structured inquiry
explore the correlation between variables
rewrite equations of volume and surface area
rewrite cost function as a function in one variable
graph the fuction and explore the graph
identify minima and attempt to evaluate it
research other possible ways to achieve better estimation
make sure you use same measurement units all the time
Guided inquiry
review rate of change of a straight line
focus on the tangent to a curve at a point
the gradient of the tangent is zero happens when?
minima
maxima
use a secant through defined and an arbitrarily close point on a curve
evaluate the limit as the arbitrary point approaches the given point on the graph
what kind of function does the limit taken result?
compare evaluated result from the structured inquiry process
reflect on the results gained
observe the findings in final inquiry steps and reflect on its importance
Open inquiry
research possible extension of usage of derivative from first principles
research concrete application
define variables, realtions among them and make a model as a function
use diagrams to visualize the model
decide on the approach to obtain the derivative function
solve the limit and discuss the results
formulate your answers using mathematical language and symbols