Increasing and Decreasing Function

Question 1. Determine where [f(x)=x^{2}-4x+1] is increasing and decreasing. Step-by-step Solution: Compute derivative: [\dfrac{d}{dx}f(x)=2x-4]. Find critical point: solve [2x-4=0] ⇒

1. Concept Overview The wavy curve method (also called the sign scheme method) is a systematic way of determining where

Question 1. Determine where [f(x)=x^{2}-4x+1] is increasing and decreasing. Step-by-step solution: [\dfrac{d}{dx}f(x)=2x-4]. Critical point: solve [2x-4=0] ⇒ [x=2]. Test intervals:

1. Concept Overview A function describes how one quantity changes with respect to another. A function can decrease, meaning its

Question 1. Determine where [f(x)=x^{3}-3x] is increasing. Step-by-step Solution: [\dfrac{d}{dx}f(x)=3x^{2}-3]. Solve [3x^{2}-3=0] ⇒ [x^{2}=1] ⇒ [x=\pm 1]. Sign chart for

1. Concept Overview A function is said to be increasing when its output rises as the input increases. Formally: A