Calcslopes & concavity
posted by Andy .
1. Let f(x)=x^33x+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?

f' = slope = 3 x^2  3
at x = 2
m = f'(2) = 3*83 = 21
y = 21 x + b
if x = 2, y = 86+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