erify that the hypotheses of the Mean Value Theorem are satisfied for each of the functions on the given intervals, and find the value of a number(s) "c" which Mean Value Theorem guarantees

Question

For the function: h(x) = sin (x) on [0, pi/2)

Answer 1

sin(0) = 0

sin(pi/2) = 1

the slope of the secant line is (1-0) / ( pi/2-0)

= 1 / (pi/2) = 2/pi

derivative is cosx ---> cos c = 2/pi

c = inverse_cos(2/pi)

= 0.8806892354203566672269437825689

and 0 < c < pi/2