contestada

Let f(x) = log(4x + 8x ln 2). For all values of a for which the function is defined, what is the instantaneous rate of change at x = a?

Respuesta :

LammettHash

[tex]f(x)=\log(4x+8x\ln2)=\log(4x(1+2\ln2))=\log4x+\log(1+2\ln2)[/tex]

The function is defined for [tex]x>0[/tex]. The derivative is

[tex]f'(x)=\dfrac4{4x}=\dfrac1x[/tex]

so for any [tex]a>0[/tex], the function's instantaneous rate of change is [tex]\dfrac1a[/tex].