Derivative at a Point: Limit Definition and Interpretation
Read this topicExplanations 9
- Let's think about how we can calculate the derivative at a point for a function y=f(x)y=f(x)y=f(x). For example, let's sketch an arbitrary graph (in this case, we use y=x2y = x^…
By Brandon Lin, Yan Yau Cheng, Moor Xu, Alex Federspiel
- I'm stealing a good amount of stuff from Brandon Lin's explanation. Let's try to calculate the derivative of f(x)=x2f(x)=x^2f(x)=x2 at x=1.x=1.x=1. So it's enough to compute the…
By Ray Li, Expii Team, Moor Xu, Victor Wang
- What is a derivative, you ask? Why, it's the instantaneous rate of change! Doesn't quite make sense yet? Ok, there are two classic ways of thinking about this: Imagine you are d…
By Rogers Epstein
- Definition of Derivative You're driving your car on a highway. Your initial position is 0, and your position as a function of time ttt is t2t^2t2. The graph below shows your car…
By Ananya Kumar
- IRoC and Rates of Change. The instantaneous rate of change measures the rate of change, or slope, of a curve at a certain instant. Thus, the instantaneous rate of change is give…
By Al, Michelle Lopez, Renee Jones, AnaMaria, James Cleveland, Victor Wang
- Instantaneous rate of change known as (IRoC) is the equivalent to finding the slope of a tangent line. For example in the image above, when the difference between the 2 points s…
By juliette, Zaire Nedd, Bintou Camara
- IROC- Instantaneous Rate Of change IROC is The rate of change at a particular moment which is the same as the value of the derivative at a particular point. For a function, the …
By tytiana baines, michelle marte, natalie woss , Amanda Berrios, James Cleveland
- Let f(x)f(x)f(x) be a function. The derivative of f(x)f(x)f(x) at x=ax=ax=a, denoted f′(a)f'(a)f′(a) is f′(a)=limh→0f(a+h)−f(a)hf'(a) = \lim_{h\to 0} \frac{f(a+h)-f(a)}{h}f′(a)…
By Noah Libby, Japheth Wood, Moor Xu
- (Video) Finding Instantaneous Rates of Change Using the Definition of Derivatives by PatrickJMT Here's a video by patrickJMT explaining how to find the instantaneous rate of cha…
By Alex Federspiel
Problems 8
- Find the instantaneous rate of change for the function f(x)=4x2+4x−3f(x)=4x^2+4x−3f(x)=4x2+4x−3 at x=5x=5x=5.
- The cost of producing a unit of goods for a factory is C(x)=3000+15x+0.03x2C(x)=3000+15x+0.03x^2C(x)=3000+15x+0.03x2. Find the instantaneous rate of change when x=300x=300x=300.
- You and a friend are planning a hike through some mountains. You know the equation for your elevation is as follows, E(t)=150x2−7.5x3E(t)=150x^2-7.5x^3E(t)=150x2−7.5x3 where xxx…
- Find the instantaneous rate of change for f(x)=5x2−6x+9f(x)=5x^2-6x+9f(x)=5x2−6x+9 at x=11x=11x=11.
- Find the instantaneous rate of change for f(x)=x3f(x)=x^3f(x)=x3 at x=6x=6x=6.
- Find the instantaneous rate of change for f(x)=8000+240x−1.25x2f(x)=8000+240x-1.25x^2f(x)=8000+240x−1.25x2 at x=50x=50x=50.
- The instantaneous rate of change for f(x)=ax2−40x+76f(x)=ax^2-40x+76f(x)=ax2−40x+76 is 888 at x=6x=6x=6. What is aaa?
- A particle follows a straight path. Its distance is given by d(t)=5+3t−0.75t2d(t)=5+3t-0.75t^2d(t)=5+3t−0.75t2 where ddd is the distance in meters and ttt is the time in seconds…