Answer to Question #156303 in Calculus for Gill Allain

Question

Given that f(x) = 6 cosh2x + 10 sinh2x - 65, x E R, solve the stationary points on the curve y = f(x). Determine also the coordinates of the point of inflexion

Answer 1

$f(x)=6\frac{e^{2x}+e^{-2x}}{2} +10\frac{e^{2x}-e^{-2x}}{2}-65=3e^{2x}+3e^{-2x}+5e^{2x}-5e^{-2x}-65=8e^{2x}-2e^{-2x}-65$

$f'(x)=16e^{2x}+4e^{-2x}$

f'(x)>0 - There is no stationary points and points of inflexion