Question

Let $f(x) = \frac{1}{3+2x}$ and point $P = (1, \frac{1}{5})$. a. Use the following definition of the slope of the tangent line at $x = a$ to find the slope of the line tangent to the graph of $f$ at $P$. $m_{tan} = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h}$ b. Determine an equation of the tangent line at $P$. a. The slope of the tangent line is $oxed{}$ (Simplify your answer.)

          Let $f(x) = \frac{1}{3+2x}$ and point $P = (1, \frac{1}{5})$.
a. Use the following definition of the slope of the tangent line at $x = a$ to find the slope of the line tangent to the graph of $f$ at $P$.
$m_{tan} = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h}$
b. Determine an equation of the tangent line at $P$.
a. The slope of the tangent line is $oxed{}$ (Simplify your answer.)

Let f(x) = (1)/(3+2x) and point P = (1, (1)/(5)).
a. Use the following definition of the slope of the tangent line at x = a to find the slope of the line tangent to the graph of f at P.
mtan = limh → 0(f(a+h) - f(a))/(h)
b. Determine an equation of the tangent line at P.
a. The slope of the tangent line is oxed (Simplify your answer.)

Added by Mark C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Charles Machakwa

Step 1

The derivative of a function f(x) at x = a is denoted as f'(a) and represents the slope of the tangent line at that point. Show more…

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La = 3: and ponm = [(-) a Use the following definition of the slope of the tangent line at x = a to find the slope of the line tangent to the graph of f at p. h - 0 b. Determine an equation of the tangent line at P. The slope of the tangent line is (Simplify your answer.