What is the value of the third-order derivative of f(x) = 5x5 - 3x3 + x when x = 2

Question

Calculus question don't understand the concept

Answer 1

Note that for f(x) = axⁿ   the derivative f'(x) = a(n)x^n-1

 

f(x) = 5x⁵ - 3x³ + x

 

f'(x) = 5(5)x^5-1 -3(3)x^3-1 + 1x^1-1 = 25x⁴-9x² + 1

 

f''(x) is the derivative of f'(x) so....

 

f''(x) = 25(4)x^4-1 - 9(2)x^2-1 + 0 = 100x³ - 18x

 

f'''(x) = 100(3)x^3-1 - 18(1)x^1-1 = 300x² - 18

 

f'''(2) = 300(2²) - 18  = 300(4) - 18  = 1200-18 = 1182