For the following function find f using the definition fx li
For the following function, find f\' using the definition f\'(x)= limit as h approaches 0 f(x+h)-f(x)/h, then determine an equation of the line tangent to the graph of f at (a,f(a)) for the given value of
f(x)= sqrt(7x+1), a=9
f(x)= sqrt(7x+1), a=9
Solution
f\' using the definition f\'(x)= limit as h approaches 0 f(x+h)-f(x)/h = sqrt[7(x+h)+1] - sqrt(7x+1)/h = 7/[2 sqrt(7x+1)] x = a, f(a) = sqrt(7a+1) Equation of tangent - y - sqrt(7a+1) = {7/[2 sqrt(7a+1)]} { x - a}
