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(a) Find the intervals on which $f$ is increasing or decreasing.(b) Find the local maximum and minimum values of $f .$(c) Find the intervals of concavity and the inflection points.$f(x)=x^{4} e^{-x}$

A. $f(x)$ is increasing on $(0,4)$ and decreasing on (-infinity,0) and $(4,$ infinity $)$B. Local minima occurs at $x=0$ and the local minimum value is 0Local maxima occurs at $x=4,$ and the local maximum value is 4.69Hint: Use 1 st derivative test along with the result from part(a)C. $f(x)$ is concave up when $x \in(-\infty, 2) \cup(6, \infty)$$f(x)$ is concave down when $x \in(2,6)$

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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you miss program, we write out forsooth on. So for pot A, we need to figure out the critical point first. So if Primakov's zero, which gives us two solutions X equals 20 on the X equals before so we can see the three sub intervals from negative infinity to zero from 0 to 4 from four to infinity on the first. Integral if prime is negative. So the function is decreasing on a second hero. If prime miss positive, the function is increasing on the last interval, if prime is less than zero, so the function is decreasing again. From here we can find a local union which is at reaches at, um X equals 20 because, um, no function decreasing for us, then you in crazy music. No commitment. So with the value of zero, because a zero and then there's a local maximum at X equals 24 because the function increasing for us then decrease you. So there's a peek at that point with every four you caused, Teoh 256 times E to the minus four. Okay. Oh, so have three. Um, so we said to the sake on maturity because zero we have X equals zero true. And the six. So we can see the three couples are for intervals from active infinity 80 from 0 to 2 from 2 to 6 And the throw six to infinity. Okay, so next If if you need to zero f stop a promise. Positive. So the functions concrete path 0 to 2. If double prime is positive, it's also come Gave up 2 to 6 if double promise negative so it can kick down. Um, and the last interval left about Prime Minister Positive. It's can't keep up. Okay? So we can grow that we have poor reflection points. So the inflection point at X equals 22 and there's one more inflection points X equals six.

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