# Calc-slopes & concavity

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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 -

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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