Question

Suppose you had an inverted “U-shaped” function. Describe what the first and second derivatives would tell you.

Answer 1

First degree DERIVATIVE tells that how a function or dependent variable changes with changes in independent variable.positive first degree DERIVATIVE tells dependent variable Increases as Independent variable Increases. negitive derivative tells function decreases as Independent variable Increases.

Second degree derivative tells rate of the change in the first DERIVATIVE..

Positive second degree DERIVATIVE means function or dependent variable is increasing at increasing rate as Independent variable Increases. or negitive means either function is decreasing or increasing at decreasing rate .

Inverted U shaped function tells as we increase independent variable , function Increase up to a certain point then start decreasing.so,

First degree DERIVATIVE will be positive till break even point and at break even point it will be zero and after that it will be negitive.

Second degree derivative will be negitive as curve is concave from origin means increasing at decreasing rate.