thanks for your help on these 2 questions

Question

Discover the derivative of this given function f(x)=x² +1/x applying the definition of derivative only.

Hence verify your result using the quotient rule of differentiation and the formula for the derivative of power functions.

An business account has a nominal annual interest rate of 3% compounded monthly. Determine the value of the monthly deposit  for the account balance after 10 years to be B₁₀  =£10,000.

Answer 1

f'(x) = lim h→0 (f(x + h) f- f(x))/h = [(x + h)² + 1/(x + h) - x² - 1/x]/h = lim h→0 (x² + 2xh + h² + 1/(x + h) - x² - x)/h = lim h→0(2x + h - 1/[(x +h)x]) = 2x - 1/x².

f(x) = x² + 1/x = 2x + (0·x - 1·1)/x² = 2x - 1/x²;

PMT = FV ·(r/n)/[(1 + r/n)^nt -1].

We have: FV = $10000, r = 0.03, n= 12; t = 10.

So, PMT = 10000(0.03/12)/[(1 + 0.03/12)¹²⁰ - 1] = $71.56

Answer 2

Hi Jose, I hope this helps you.