Question

the function \\(f(x) = 2x^3 - 36x^2 + 210x + 5\\) has derivative \\(f(x) = 6x^2 - 72x + 210\\).

f(x) has one local minimum and one local maximum.

f(x) has a local minimum at \\(x\\) equals

with value

and a local maximum at \\(x\\) equals

with value

Explanation:

Find critical points

Using the Critical Points knowledge point

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LATEXBLOCK0
$$

Classify local extrema

Using the Local Extrema knowledge point

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LATEXBLOCK1
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Calculate local minimum value

Using the Local Extrema knowledge point

$$
LATEXBLOCK2
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Calculate local maximum value

Using the Local Extrema knowledge point

$$
LATEXBLOCK3
$$

Answer:

The function \(f(x) = 2x^3 - 36x^2 + 210x + 5\) has derivative \(f'(x) = 6x^2 - 72x + 210\).

\(f(x)\) has one local minimum and one local maximum.

\(f(x)\) has a local minimum at \(x\) equals <blank>7</blank>

with value <blank>397</blank>

and a local maximum at \(x\) equals <blank>5</blank>

with value <blank>405</blank>