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  • Absolute maximum and minimum? - Socratic
    (-pi 4,-1) is the minimum (pi 8,sqrt2 2) is the maximum Maximum and minimum values of a curve may be one of the critical points Critical points are points where the instantaneous rate of change is zero or undefined We have: f(x)=sin(2x) Let's find its derivative =>f'(x)=d dx(sin(2x)) Recall that: d dx(sinx)=cosx d dx(g(h(x)))=g'(h(x))*h'(x) Therefore: f'(x)=cos(2x)*d dx(2x) Now recall the
  • How do you differentiate g(x) = 2xe^(2x) using the product rule . . .
    f=2x,g=e^(2x) ->f'=2,g'=2e^(2x) g'(x)=fg'+gf'=4xe^(2x)+2e^(2x) Separate the products into f and g then find each of their derivative before putting it into the product rule
  • What is the period of #f(t)=sin( 11t)#? - Socratic
    The period of sin (kt) is 2pi k Answer: 2pi 11 x = Sin (t) graph is a series of continuous and periodic waves touching x - 1 and x = 1 The values repeat in an interval of 2pi for t, since sin (2pi + t ) = sin ( t ) Here, the period is shortened to 2pi 11 due to scaling of t by 11





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