R Programming: single-dimensional gradient descent routine to find local minima and maxima of a function on an interval

A. Write a routine to find the minima and maxima of the function () = [10, 10]

B. There are 16 minima and 15 maxima on this interval (see the plot below).

C. This is well-behaved; it is continuous and infinitely differentiable. The derivative of this function is

D. Your program should find all the minima and maxima. Finally, your program should identify the global miminum and maximum.

sin(5.c) df5cos5. dr . .5. -- sin mune -2 - - 10 -8 6 4 2 0 2 4 6 8 10 sin(5.c) df5cos5. dr . .5. -- sin mune -2 - - 10 -8 6 4 2 0 2 4 6 8 10