High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ For the function [tex]f(x) = x^5 - 5x^4 + 15[/tex], what are the 1st and 2nd derivatives?

1) [tex]f'(x) = 5x^4 - 20x^3, \quad f''(x) = 20x^3 - 60x^2[/tex]

2) [tex]f'(x) = 5x^4 - 20x^3, \quad f''(x) = 5x^3(x-4)[/tex]

3) [tex]f'(x) = 4x^3 - 20x^3, \quad f''(x) = 20x^3 - 60x^2[/tex]

4) [tex]f'(x) = 4x^3 - 20x^3, \quad f''(x) = 5x^3(x-4)[/tex]

Answer :

Final answer:

The first derivative of the function f(x) = x⁵ - 5x⁴ + 15 is f'(x) = 5x⁴ - 20x³ and the second derivative is f''(x) = 20x³ - 60x².

So, the correct answer is option 1.

Explanation:

The question is asking about the first and second derivatives of the function f(x) = x⁵ - 5x⁴ + 15. To find the derivative of the function, we can use the power rule which states that the derivative of xⁿ is n*xⁿ⁻¹.

Applying this rule, the first derivative, f'(x), becomes 5x⁴ - 20x³.

The second derivative, f''(x), is calculated by finding the derivative of the first derivative, giving us 20x³ - 60x².

The correct answer among the options you've given is therefore: f'(x) = 5x⁴ - 20x³, f''(x) = 20x³ - 60x².

Learn more about Derivatives here:

https://brainly.com/question/30365299

#SPJ11

Other Questions