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If a firm is trying ti maximize profit, it will always sell more output at a higher price? assuming it's linear curve? is it ture? or sell more output at a less price?

Answer:
The law of demand says that ceteris paribus (all other things equal) consumers will demand more at lower prices. Whether the firm increases or decreases price to make more profit depends on the elasticity of demand. If there is high price elasticity of demand (consumers are very responsive to price changes) then lowering the price will make you more money because consumers will notice and switch to your product.
If there is low price elasticity of demand (consumers arent very responsive to price changes) then an increase in price would be the way to for the firm to make money because few consumers will stop buying your product and you will earn more per unit sold to compensate for them leaving and make more profit.

I'd say sell more output at a less price but then again I only have an 8th grade education so don't bank on what I say.

All else equal- this is a key assumption- the answer is yes. If there is an outward shift in the demand curve, then the new market clearing price increases.

HOWEVER, if there is a shock to the production technology or resources that shifts the marginal cost curve up, then it is possible that a firm's new profit maximizing Q is less than its old profit maximizing Q, even if the market clearing price increases.

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