Since Bella is apparently trying to confirm that girls suck at math, I'll try to help you out. Here is my solution:
d/dx(cos(pi x)) = -pi*sin(pi x). Now, recall that the derivative tells you the rate of change of f(x) at any value of x. The nice thing about this problem is that we're confined to the interval [0, 1/4], which means the the argument of the sine function ranges from 0 to pi/4. You know that the sine of any number in this range is a positive number, which means that the derivative is negative in this range (since there's a minus sign in the derivative). If the function is constantly either increasing or decreasing throughout the entire interval that we're restricted to, then the absolute extrema are by definition the same as the bounds of the interval. So, the extrema are at x=0 and x=1/4. The corresponding y values can be found by plugging these into the original function, so you'd get y=cos(0)=1 and y=cos(pi/4)=sqrt(2)/2.
So, the coordinates for the extrema are (0,1) and (1/4,sqrt(2)/2).
Comments
Since Bella is apparently trying to confirm that girls suck at math, I'll try to help you out. Here is my solution:
d/dx(cos(pi x)) = -pi*sin(pi x). Now, recall that the derivative tells you the rate of change of f(x) at any value of x. The nice thing about this problem is that we're confined to the interval [0, 1/4], which means the the argument of the sine function ranges from 0 to pi/4. You know that the sine of any number in this range is a positive number, which means that the derivative is negative in this range (since there's a minus sign in the derivative). If the function is constantly either increasing or decreasing throughout the entire interval that we're restricted to, then the absolute extrema are by definition the same as the bounds of the interval. So, the extrema are at x=0 and x=1/4. The corresponding y values can be found by plugging these into the original function, so you'd get y=cos(0)=1 and y=cos(pi/4)=sqrt(2)/2.
So, the coordinates for the extrema are (0,1) and (1/4,sqrt(2)/2).
Yes