Question

Given that f (−0.5) = 2 and f ′(−0.5) = 4 , using a tangent line approximation you would estimate f (0) to be:

Answer 1

@dumbcow @whpalmer4

Answer 2

so figure out the equation of the line that has slope = 4 and goes through the point (-0.5, 2). then evaluate it at x=0 to estimate f(0)

Answer 3

Would that be the tangent line?

Answer 4

what I drew is the tangent line, and yes, the equation is that of the tangent line.

Answer 5

you're hopefully doing the approximation close enough that the tangent line and the actual function don't diverge very much by the time you get to the point where you do the approximation

Answer 6

f(0) = 1 ? I am not guessing, I would tell you how I came to it but I don't know how to process the thought out lol

Answer 7

Oh, come on...if at x = -0.5, the value of f(x) = 2, and it is increasing at a rate of 4 per unit of x, how could it only 1 at x = 0 ?!? The slope would have to be -4 to accomplish that...


\[y-y_1 = m(x-x_1)\]is the point-slope form. You have \(m=4\), and \((x_1,y_1) = (-0.5,2)\)