Question

(a) Find the maximum and minimum values of f(x) = 3x 3 − x on the closed interval [0, 1] by the following steps:

i. Observe that f(x) is a polynomial, so it is continuous on the interval [0, 1].

ii. Compute the derivative f 0 (x), and show that it is equal to 0 at x = 1 3 and x = − 1 3 .

iii. Conclude that x = 1 3 is the only critical number in the interval [0, 1].

iv. Compute the values f(0), f(1), and f( 1 3 ); and indicate the maximum and minimum values of f(x) on [0, 1].

(b) Find the absolute maximum and minimum values of F(x) = x + 9 x on the closed interval [1, 20]. HINT: Use the same steps as the previous problem

Answer 1