Problem: find the value of $x$ that maximizes $$f(x) = \log (-20x + 12\sqrt{x}).$$ if there is no maximum value, write "none".

The value of x is 0.09

Step-by-step explanation:

Here, the given function is,

Differentiating with respect to x,

Again differentiating with respect to x,

For maxima or minima,

At x = 0.09,

f''(x) = negative,

Hence, for x = 0.09, f(x) is maximum.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

true

step-by-step explanation:

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