Let f(x) = -x^2+2x-3 Find the slope of the tangent line of the graph of f(x) at x=c.

Question

Find the average rate of change of the graph of f between x=c and c+h.

Find the slope of the tangent line of the graph of f(x) at x=c.

Answer 1

Since  x=c  , then   c+h = x+h
 
f(x) = -x²+2x-3
 
f(x+h) = -(x+h)² + 2(x+h) -3
 
For part a)
[f(x+h)-f(x)]/[(x+h)-x)]
 
 
Part b)
Use the difference quotient
 
lim [f(x+h) - f(x)]/h        as h approaches zero.