Yefim S. answered • 08/05/20

Math Tutor with Experience

Let consider function y = 7x - 2sinx + 4. Now derivative y' = 7 - 2cosx > 0 for all x. So y is increasing function.

Now for x = - π/2 y = 7(-π/2) - 2sin(- π/2) + 4 = - 7π/2 + 6 < 0 and for x = 0 y = 7·0 - 2sin0 + 4 = 4 > 0.

Then thetre is just 1 value of x where y = 0.

By Intermediate Value Theorem this equetion has only one solution, becouse exist some x_{0 }between -_{ }π/2 and 0 where y = 0 and this x0 is unique because y is increasing function..