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

0
1
–2
–3
4

Answer 2

Do you understand what that all means?

Answer 3

Not really.

Answer 4

You can use the equation of a line to make your 'linear approximation' .
y - y1 = m( x - x1)
Suppose
x1 = -0.5
y1 = f(-0.5)= 2
m = f ' (-0.5)=4

We have
y - 2= 4 ( x - (-.5))
y = 4( x + .5) + 2

now plug in x = 0

Answer 5

y=2

Answer 6

y=4
sorry

Answer 7

The tangent line gives us the slope of the curve at that very point. So if we know the value of our function somewhere nearby, and the slope of the tangent line at that point nearby, we can estimate the value of the function at our point of interest.

Answer 8

you can also solve this using
delta y ≈ f ' (x) * delta x

Answer 9

we estimate f(b) as (b-a) * f'(a)+ f(a)