Calculus | Senioritis

John Rhodes
June 21, 2023
Calculus

Finding Maximum Rate Of Change: Derivatives And Analysis Of Mathematical Functions

Find max rate of change Magnitude of gradient vector To find the maximum rate of change, we need to take the derivative of the function and then...

John Rhodes
June 21, 2023
Calculus

How To Perform The Second Derivative Test To Find Critical Points Of A Function: Steps And Guidelines

Second Derivative Test D(x,y) = fxx(x,y) * fyy(x,y) – (fxy(x,y))^2 – D(x,y) > 0, fxx(x,y) > 0 => local maximum – D(x,y) > 0, fxx(x,y) < 0...

John Rhodes
June 21, 2023
Calculus

The Fundamental Theorem For Extreme Values: Maximum And Minimum Values Of Continuous Functions On Closed Intervals

Extreme Value Theorem If f is continuous on [a,b] then f has an absolute maximum and an absolute minimum on [a,b]. The global extrema occur at critical...

John Rhodes
June 21, 2023
Calculus

Maximizing Math: A Comprehensive Guide To Finding Extrema Of Univariate Functions

Find extrema Set fx(x,y) and fy(x,y) to 0, plug in boundaries of x and y into original function. To find the extrema of a function, you need...

John Rhodes
June 21, 2023
Calculus

Maximize And Minimize Functions: A Step-By-Step Guide With An Example

Find max/min value Plug point original function To find the maximum or minimum value of a function, we need to take the derivative of the function and...

John Rhodes
June 21, 2023
Calculus

Calculating Riemann Sum Approximation For Integral Of F(X) Using 3 Intervals: A Math Tutorial

Let f be the function given by f(x)=x2+1x√+x+5. It is known that f is increasing on the interval [1,7]. Let R3 be the value of the right...

John Rhodes
June 21, 2023
Calculus

Midpoint Riemann Sum For Math: Calculating Absolute Difference

Let f be the function given by f(x)=x2e−x. It is known that ∫10f(x)ⅆx=0.160603. If a midpoint Riemann sum with two intervals of equal length is used to...

John Rhodes
June 21, 2023
Calculus

How To Find The Relative Maximum Of A Function Using Calculus: A Step-By-Step Guide

Let g be the function defined by g(x)=∫x−1(−12+cos(t3+2t))ⅆt for 0