Solution Found!
Calculating derivatives f(x+h)f(x) a. or the following
Chapter 4, Problem 49E(choose chapter or problem)
Calculating derivatives
a. For the following functions, find f’ using the definition
\(f'(x)=\lim _{h \rightarrow 0}\ \frac{f(x+h)-f(x)}{h}\)
b. Determine an equation of the line tangent to the graph of f at (a, f(a)) for the given value of a.
\(f(x)=\sqrt{3x-1};\ \ a=8\)
Questions & Answers
QUESTION:
Calculating derivatives
a. For the following functions, find f’ using the definition
\(f'(x)=\lim _{h \rightarrow 0}\ \frac{f(x+h)-f(x)}{h}\)
b. Determine an equation of the line tangent to the graph of f at (a, f(a)) for the given value of a.
\(f(x)=\sqrt{3x-1};\ \ a=8\)
ANSWER:SOLUTION STEP 1 (a). Given f(x) = 3x+1. We need to find the derivative of f(x) using the definition of the derivative f(x+h)f(x) The definition of the derivative is(x) = lim h h0 f(x+h) = 3x+h)+1 3(x+h)+1 3x+1 Thus f (x) = lim h h0 To solve this we have to multiply the numerator and the denominator with the conjugate of the numerator. 3(x+h)+1 3x+1