Question

Having a hard time grasping the concept of curve sketching. Please help. I'm a little confused.

Answer 1

Do you mean sketching a curve given information about the curve, or sketching the curve after being given the function? The second would require you to find the information about the curve, which tells you what the function looks like.

Answer 2

its for calculus. One of the question gives the graph of the derivative and asks for when the function is increasing and decreasing. I know that I would have to look at were the function is going up or down if it asks for increase and decreasing and below or above the x-axis if it asks for positive or negative. My question is that if I am give the graph of a derivative and asked when the function is increasing or decreasing would I look at when the derivative is above or below the x-axis

Answer 3

A function \(f(x)\) is increasing over an interval if \(f'(x)>0\) on that interval. Similarly,
a function \(f(x)\) is decreasing over an interval if \(f'(x)<0\).

Basically, if you're given a graph like this, you have to look for where f '(x) is positive or negative.