In calculus, it is known that the rate of change of the function f(x) = tan x is sec2 x.......?

Question

In calculus, it is known that the rate of change of the function
f(x) = tan x is sec2 x.
If x is on the interval [0, 2π), determine the values of x for which the rate of change is 5. Round to three decimal places. Convert secant to cosine if you prefer. (Enter your answers in radians. Enter your answers as a comma-separated list.)

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Answer 1 · 2018-06-06T14:09:06

#x=arccos(sqrt(1/5))+2pin,2pi-arccos(sqrt(1/5))+2pin#

If the rate of change for #tan(x)# is #5#, then the derivative of #tan(x)# is equal to #5# on those values.

So, we get:

#d/dx(tan(x))=5#

#sec^2(x)=5#

#1/(cos^2(x))=5#

#cos^2(x)=1/5#

#cos(x)=+-sqrt(1/5)#

#:.x=arccos(sqrt(1/5))+2pin,2pi-arccos(sqrt(1/5))+2pin#