The directions state, a. Find the difference quotient of f.
b. f'(c) by comparing the limit of the difference quotient. Also, c is a constant.
h=change in x.
1.f(x)=f(x)=2-x^2 at c=0. the answer states: for a. -h and b. 0. For everytime I did the derivative formula, I get (2x-h). But when i plug 2 in for x and x^2 for h, it gets the right answer and that is what got me confused. Is it alwayz the case to use h when doing the derivative formula? If not, what are the exceptions?
2. Find the standard form equation for the tangent line to y=f(x)at the specified point.
f(x)= (x^2)-3x-5 where x=-2, the answer states:7x+y+9=0 I would know what rule to use if it had only an f(x) and a g(x). But on this one, I am not too sure.
3. Find the coordinates of each point on the graph of the given function where the tangent is horizontal.
f(x)=2x^3-7x^2+8x-3. the answer states: (1,0) and (4/3,-1/27). Same problem as #2 but not sure on the latter steps sense it is in coordinate form.