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Suppose the derivative of a function $f$ is $f^{\prime}(x)=(x+1)^{2}(x-3)^{5}(x-6)^{4} .$ On what interval is $f$ increasing?

$f(x)$ is increasing for $x \in(0,3)$

Calculus 1 / AB

Chapter 4

APPLICATIONS OF DIFFERENTIATION

Section 3

Derivatives and the Shapes of Graphs

Derivatives

Differentiation

Applications of the Derivative

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In mathematics, a derivati…

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Suppose that the function …

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Determine the interval(s) …

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determine where $f(x)$ is …

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If $ \displaystyle f(x) = …

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Increasing and decreasing …

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Find the intervals on whic…

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Use the graph of the funct…

for this pro program. We just said I have primary cause zero. So we have ah, three solutions. X equals two minus one. X equals 23 and the X equals 26 There's on this solutions with separates the the domain toe four different parts negative. Infinity to minus 91. Negative. 123 3 to 6 in the six to infinity on the first interval. Let's look at the quality for negative off if prime, um, component wisely. That means, uh, because the if promise given so we can ride out each off its components like this. Okay, now we can tow finish this table. So for the if access in negative infinity to negative one, this part is positive. The second part is negative. The last part is positive because of the Paris For So we can crew that if promise negative. And the them is the function is decreasing on the second. Terrible. The first part is positive. Uh, the second part. It's also negative. Last carats positive. So we can cruel that if promise Negative. So the function is decreasing. Um oh, for the 30 number from three. Toe to six on the first pie partly if the second had positive in the last part is also positive because the power is for so the function is increasing. And for the last interval off, then my positive. So the function is increasing, so the increasing Tebow should be from the read to infinity.

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