[SOLVED] Math 240 — hw 1

1. Given the function f(x) = x
2 + 2x+ 1, estimate f
′
(2) using the points (1, 4) and (2, 9).
The actual answer is 6–how close is your estimate?
2. For the function f(x) = sin(x), estimate f
′

π
7


using the points
π
6
,sin(π
6
)


and

π
4
,sin(π
4
)


. How good is your estimate?
3. For the function f(x) = √
x, estimate f
′
(0.5) using the points (0, 0) and (1, 1). How
good is your estimate?
4. Using the table below for f(x), estimate f
′
(1.5).
x f(x)
1 2
1.5 2.25
2 2.5