Name 1. Explain why the function f(x) = x' +3x -2 has a zero on the interval [o, 1]. F ( x ) = * 3 + 3x- 2 F(o ) = 05 + 3 ( 0 ) - 2 20 F ( ) = 13 + 3() - 270 F( x ) is continuous, F(o)60, and F () 70 by lut there exists a c on ( Oil) such that F(c ) = 0 2. Verify that the Intermediate Value Theorem applies to the function f(x) = x2 + x-1on the interval [0,5] and f(c) =11. Find the value of c guaranteed by the theorem. F(x) =x2+ x -I on [o.5] , F()=1 F ( 0 ) = 11 F ( 5 ) = 3. Let f(x) be a continuous function for all real numbers. The table below gives values of f for selected values of x. x -6 2 5 9 15 f (x ) 11 -4 10 13 8 On -6