Interpreting the Sign of the First Derivative (Increasing and Decreasing Functions)
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Differential Calculus #12: Intro to Graphing Derivatives
Key Questions

Answer:
If
#x_0 < x_1# then#f(x_0) < f(x_1)# Explanation:
The meaning is that you have a function with positive slope in every point of Dom.
Starting from a
#x_0# and move to right, the graph of function is moving up at the same time 
Answer:
It will be increasing when the first derivative is positive.
Explanation:
Take the example of the function
#f(x) = e^(x^2  1)# .The first derivative is given by
#f'(x) = 2xe^(x^2  1)# (chain rule). We see that the derivative will go from increasing to decreasing or vice versa when#f'(x) = 0# , or when#x= 0# .Whenever you have a positive value of
#x# , the derivative will be positive, therefore the function will be increasing on#{xx> 0, x in RR}# .The graph confirms
Hopefully this helps!

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Videos on topic View all (20)
Graphing with the First Derivative

1Interpreting the Sign of the First Derivative (Increasing and Decreasing Functions)

2Identifying Stationary Points (Critical Points) for a Function

3Identifying Turning Points (Local Extrema) for a Function

4Classifying Critical Points and Extreme Values for a Function

5Mean Value Theorem for Continuous Functions