Question

If the following function is continuous, what is the value of a + b?
f(x) = {3x^2 - 2x +1, if x < 0
a cos(x) + b, if 0 </= x </= pi/3
4sin^2(x), if x > pi/3

A. 0
B. 1
C. 2
D. 3
E. 4

I know that since the function is continuous, it should be equal to 1 at 0 and 3 at pi/3 (To follow the other two pieces of the function). From here, I am having a great deal of difficulty figuring out what coordinates would make the function work in this way. Any help is appreciated.

Answer 1

At x=0, a*cos(0)+b = 1 = 3x^2-2x+1
=> a+b= 1 = 3(0)-2(0)+1

At x=π/3,
a*cos(π/3) + b = 1 = 4sin^2(π/3)
=> (a/2) + b = 3/2 = 2*3/4

But you don't need to solve for a and b if only a+b is required. (see second line).