Posted by **Andy** on Sunday, January 23, 2011 at 5:05pm.

1. Let f(x)=x^3-3x+2

a.) Find the equation of the line tangent to the graph of y=f(x) at x=2

b.) For what values of x is the function increasing?

c.) For what values of x is the graph concave down?

- Calc-slopes & concavity -
**Damon**, Sunday, January 23, 2011 at 6:21pm
f' = slope = 3 x^2 - 3

at x = 2

m = f'(2) = 3*8-3 = 21

y = 21 x + b

if x = 2, y = 8-6+2 = 4

4 = 21(2) + b

4 = 42 + b

b = -38

so

y = 21 x - 38

b.

3 x^2 - 3 where is that + ???

with big + or - x, slope big +

0 = 3 x^2 - 3

x = +/- 1

so only - between -1 and + 1

-1> x >1

c.

where is f" negative?

f"(x) = 6x

for negative x f"(x) is negative

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