Question

find an equation of the line tangent to the graph of f(x) = 1/x^6
a) at (1,1)
b) at (3, 1/729)
c) at (-2, 1/64)
a) the equation of the tangent line at (1,1) is
(type an equation using x and y as the variables.)

Explanation:

Step1: Find derivative of $f(x)$

$f'(x)=-\frac{6}{x^{7}}$

Step2: Evaluate derivative at $x = 1$

$f'(1)=-6$

Step3: Use point - slope form

$y - 1=-6(x - 1)$
$y=-6x + 7$

Answer:

$y=-6x + 7$