Question

Would you be able to help me with a couple of questions? thanks in advanced!

1. I am given the graph f(x)=x^2-2x. I have to draw a line tangent to the point (0,0). Then, I have to estimate the slope at that point.

how would I go about answering this question? would I first find the slope? also how do you estimate the slope at that point?

2. Use the alternate definition, lim x->a f(x)-f(a)/x-a, to determine the instantaneous rate of change of f(x)= 1/x at the point (1,1/5)

For this question, I got b but I am not sure it is correct

Answer 1

you know the slope of the tangent for
y = f(x) at any point is
m = dy/dx

So, for y = x^2-2x, the slope at any x is
y'(x) = 2x - 2
So, at (0,0), mm = -2

If you want to estimate the slope, pick two x values close to zero and find the slope between those two points on the curve.

For example, if you pick -.1 and +.1, then
f(.1) = -.19
f(-.1) = .21
and the slope between (-.1,.21) and (+.1,-.19) is -.4/.2 = -2

No idea what "b" means for #2.