5. (8 pts) Compute the derivative of h(x) = x^3+x^2/e^3x
and simplify your answer.

  h'(x) = (-3x^3 +2x)/e^(3x)

Step-by-step explanation:

The formula for the derivative of a quotient is ...

  (u/v)' = (vu' -uv')/v²

Using u = (x^3 +x^2) and v = e^(3x), this becomes ...

  h'(x) = (e^(3x)(3x^2 +2x) -(x^3 +x^2)(3)(e^(3x))/e^(6x)

  h'(x) = (-3x^3 +2x)/e^(3x)

part a

x     y

0     8

1     7.5

2     7

3     6.5

4     6

5     5.5  

for every hour i deducted .5 inches from the length of the candle

part b

it is a function because for every x value there is only one y value

part   c

for every x value there is only one y value

x       y

0       8

1       7.6

2       7.2

3       6.8

step-by-step explanation:

b. x + 1

step-by-step explanation:

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