Question

Suppose the function f(x)=4/x
a) Use the definition of the derivative to show that f ' (-2) = -1.
b) Write an equation for the line tangent to the graph of f at x = -2.

Answer 1

f(-2) = 4/-2 = -2
f(-2+h) = 4/(-2+h)

f(-2+h)-f(-2) = 4/(-2+h) + 2
= [ 4 -4+2h ] / (-2+h)
= 2 h /(-2+h)

[f(-2+h)-f(-2)]/h = 2/(-2+h)
limit as h -->0 = 2/-2 = -1

b)
slope = m = -1
y = -x + b
goes through (-2, -2)
-2 = 2 + b
b = -4
y = -x -4

Answer 2

what is h?