Question

Use the first derivative to determine where the function

f(x)= -15x^2-10x+6

is increasing and decreasing.
Use interval notion. Use U for a union (more than one interval) and leave it blank if the interval is the empty set.

Answer 1

So, we have:
\[
f(x)=-15x^2-10x+6
\]Thus:
\[
f'(x)=-30x-10
\]So, we have points of inflection at:
\[
f'(x)=-30x-10=0\implies\\
x=-\frac{1}{3}
\]Using the second derivative test, we have:
\[
f''(x)=-30<0
\]So it is a local maxima, which means that the function is increasing steadily until \(x=-\frac{1}{3}\), where it has an inflection point, and then steadily decreases. Et al.

Answer 2

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Answer 3

Haha, sure thing.