CALCULUS DERIVATIVES

Question

Calculate (y^(k))(0) for 0 is less than or equal to k which is less than or equal to 5, where y=5x^4+ax^3+bx^+cx+d (with a, b, c, d the constants)

Answer 1

So we need the first 5 derivatives

 

 f(0) =  d

 

 f'(x) = 20x^3 + 3a x^2 + 2b x + c  ----> f'(0) = c

 

f''(x) = 60x^2 + 6a x + 2b --->  f''(0) = 2b

 

f'''(x) = 120x + 6a ---> f'''(0) = 6a

 

f''''(x)  = 120 ---> f''''(0) = 120

 

f'''''(x) = 0 for any x