Question

need help finding local extrema, inflection points, and x and y intercepts when they exist

Answer 1

post away.

Answer 2

\[f(x)=\frac{1}{15}x^3-x+1\]

Answer 3

when x is 0 y is 1 so I know that the y-intercept is (0,1)

Answer 4

okay for local extrema:
first derivative
for inflections:
second derivative
for y-int:
set x = 0, solve for y
for x-int:
set y=0, solve for x

Answer 5

for the first derivative I got
\[f \prime (x)=\frac{1}{5}x^2-1\]

Answer 6

Let's find the extrema first:
f'(x) = (3/15)x^2-1 = 0
f'(x) = (x^2)/5 - 1 = 0
x^2 - 5 = 0
x^2 = 5
x = +/-5