Differentiate y=2/x^3-4x^5+x^pi-4x+1

Thread starter ttpp1124
Start date Apr 24, 2020
Tags

Differentiate

In summary, the conversation discusses a polynomial function with multiple terms, including a constant, variable terms with exponents, and a term with pi as an exponent. The degree of the polynomial is 5, and to differentiate it, the power rule can be used. The derivative of the function represents the slope of the tangent line, and the critical points can be found by setting the derivative equal to 0 and solving for x.

Apr 24, 2020

ttpp1124

Homework Statement: Is this correct? Not sure if it's formatted right...

Relevant Equations: n/a

Physics news on Phys.org

Apr 24, 2020

.Scott

Science Advisor

Homework Helper

You got it!

Related to Differentiate y=2/x^3-4x^5+x^pi-4x+1

1. What is the first derivative of y=2/x^3-4x^5+x^pi-4x+1?

The first derivative of y=2/x^3-4x^5+x^pi-4x+1 is y'=-6/x^4-20x^4+pi*x^(pi-1)-4.

2. How do you find the critical points of y=2/x^3-4x^5+x^pi-4x+1?

To find the critical points of y=2/x^3-4x^5+x^pi-4x+1, set the first derivative equal to 0 and solve for x. Then, plug these values into the second derivative to determine if they are maximum, minimum, or inflection points.

3. What is the second derivative of y=2/x^3-4x^5+x^pi-4x+1?

The second derivative of y=2/x^3-4x^5+x^pi-4x+1 is y''=24/x^5-80x^3+pi*(pi-1)*x^(pi-2).

4. How do you determine the concavity of y=2/x^3-4x^5+x^pi-4x+1?

To determine the concavity of y=2/x^3-4x^5+x^pi-4x+1, plug the critical points and any other important points into the second derivative. If the result is positive, the function is concave up. If the result is negative, the function is concave down.