2 years ago

Solve using logs 5^(3x-6)=125

Mathematics

1 answer:

Hitman42 [59]2 years ago

3 0

$5 ^{3x-6} =125 \\ \\ 5 ^{3x-6} =5^3 \\ \\3x-6 =3 \ \ |+6 \\ \\3x=3+9 \\ \\3x=12 \ \ /:3 \\ \\x=\frac{12}{3} \\ \\x= 3$

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What is the maximum number of relative extrema contained in the graph of this function f(x)=3x^3-x^2+4x-2

Sergeeva-Olga [200]

The maximum number of turning points in a cubic function is 2.

In this case,

$f(x)=3x^3-x^2+4x-2\implies f'(x)=9x^2-2x+4$

The discriminant is $(-2)^2-4(9)(4)=-140$ , which means the derivative has no real roots. This means there are no critical points and thus no turning points/relative extrema.