For f x x3 2x2 7 use the Intermediate Value Theorem to de

For f (x) = x³ – 2x² – 7, use the Intermediate Value Theorem to determine which interval must contain a zero of f.              (no explanation required)                                  3. _______

A.        Between 0 and 1

B.        Between 1 and 2

C.        Between 2 and 3

D.        Between 3 and 4

Solution

f(x) = x^3 -2x^2 -7

By Intermediate Value Theorem If the function is negative and then becomes positive it must pass thru zero

Between 0 and 1 ; f(0) = -7 ; f(1) = 1-2 -7 = -8

Between 1 and 2 : f(1) = -8 ; f(2) = 8 -2*4 -7 = 8 -8 -7 =-7

Between 2 and 3 ; f(2) = -7 ; f(3) = 27 - 2(9) -7 = 2

Between 3 snd 4 : f(3) = 2 ; f(4) = 64 - 32 -7 = 25

We can see between 2 and 3 function becomes from -ve to +ve so, funcyion passes through

0. Hence Option C