Use the first derivative test to find the location of all local extrema in the interval (0,2) for the function given below. f(x) = -5x^6ln(2x) If there is more than one local maximum or local minimum, write each value of x separated by a comma. If a local maximum or local minimum does not occur on the interval, enter ∅ in the appropriate box. Enter exact answers. The local maxima occur at x = _. The local minima occur at x = _.

Name: use the first derivative test to find the location of all local extrema in the interval 02 for the function given below fx5x6ln2x if there is more than one local maximum or local minimum wri 14193
Uploaded: 2022-03-19T05:56:36-08:00
Duration: 3 min 45 s
Channel: Suman Saurav Thakur
Description: use the first derivative test to find the location of all local extrema in the interval 02 for the function given below fx5x6ln2x if there is more than one local maximum or local minimum wri 14193

          Use the first derivative test to find the location of all local extrema in the interval (0,2) for the function given below.
f(x) = -5x^6ln(2x)
If there is more than one local maximum or local minimum, write each value of x separated by a comma. If a local maximum or local minimum does not occur on the interval, enter ∅ in the appropriate box. Enter exact answers.
The local maxima occur at x = _____. The local minima occur at x = _____.

Added by Gloria D.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Suman Saurav Thakur

03/19/2022

Step 1

\[ f'(x) = -30x^5 \ln(2x) + 6x^4 = 0 \] \[ 6x^4(5 - 5x\ln(2)) = 0 \] This gives us critical points at \(x = 0\) and \(x = \frac{1}{2}\). ** Show more…

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Use the first derivative test to find the location of all local extrema in the interval (0,2) for the function given below. f(x) = -5x^6ln(2x) If there is more than one local maximum or local minimum, write each value of x separated by a comma. If a local maximum or local minimum does not occur on the interval, enter ∅ in the appropriate box. Enter exact answers. The local maxima occur at x = _____. The local minima occur at x = _____.