Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. (Simplify your answers completely.) f(x) = −19

Question

Step 1: f(x+h)=

Step 2: (f(x+h)-f(x)=

Step 3: f(x+h)-f(x)/h=

Step 4:f '(x) = lim h→0 f (x + h) − f(x)/h

=

Answer 1

f(x)= -19 (constant function--no matter the input the output is -19)

So,

f(x+h) = -19

f(x) = -19

f(x+h) - f(x) = -19 - (-19) = 0

[f(x+h) - f(x)] / h = 0/h = 0

lim_h->0 0 = 0 (limit of a constant = constant).

Answer 2

f(x + h) = -19 + h

f(x + h) - f(x) = -19 + h - (-19)

f(x + h) - f(x) = h

[f(x + h) - f(x)] / h = h / h

lim h → 0 h / h = 0