Cooper Section $8\mathrm{.}12$ #$10$

Suppose that $f(x)=2x^3-3x^2-36x+3.$

$a.On$ which intervals $isf(x)$ increasing? $(Use$ I for infinity and $-$I for negative infinity.$)$ Enter the

intervals $in$ increasing order.

$(x-3)(x-1)x>3x<mn>1</mn><mi>f</mi><mi>(</mi><mi>x</mi><mi>)</mi>$

Hint: When $is(x-3)(x-1)$ positive? The product $of$ two numbers $is$ positive $if$ either they

are both positive $or$ else $if$ they are both negative. They are both positive when $x>3$ and they

are both negative when Conclusion: Factor the derivative. $Itis$ something like this, but

different.

$b.$ Where $isf(x)$ concave $up?$

and

Hint: When $is(x-3)(x-1)$ positive? The product $of$ two numbers $is$ positive $if$ either they

are both positive $or$ else $if$ they are both negative. They are both positive when $x>3$ and they

are both negative when Conclusion: Factor the derivative. $Itis$ something like this, but

different.

$b.$ Where $isf(x)$ concave $up?$