Difference Quotient

Question

Calculate the difference quotient for f(x)=1/√(2x+5) at a=4.

f(4+h)-f(4)/h= ?

Answer 1

The difference quotient f(4+h)-f(4)/h when h is very small (lim _h-->0 f(4+h)-f(4)/h) is equivalent to the derivative of the function f(x)=1/√(2x+5) calculated at x=4. The derivative of the function f(x)= 1/(2x+5)^-(1/2) is calculated as f'(x)= -1/(2x+5)^-(3/2), finding f'(4)=-1/13^(-1/3) = -0.425.