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Numerade Educator

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Problem 43 Medium Difficulty

(a) Graph the function
$ f(x) = x^4 - 3x^3 - 6x^2 + 7x + 30 $
in the viewing rectangle [-3,5] by [-10,50].
(b) Using the graph in part (a) to estimate slopes, make a rough sketch, by hand, of the graph of $ f' $.
(c) Calculate $ f'(x) $ and use this expression, with graphing device, to graph $ f' $. Compare with your sketch in part (b).

Answer

(a)
(b) Positive (so $f^{\prime}$ is positive) on $\left(x_{1}, x_{2}\right)$ and $\left(x_{3}, \infty\right)$
(c) $$f^{\prime}(x)=4 x^{3}-9 x^{2}-12 x+7$$

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Video Transcript

Hey, it's close when you read here. So for part A, I'll draw our graph, and it looks something like this for part B. We have All right, um, graph of our original and then we're gonna graph are derivative. I'll do it in green. So you have. And then you finally, for part C, we're going to find our We're gonna difference she our original function and we get this is equal to for X cubed minus nine X square minus 12 x my seven. And when we grab this, I look like this.