Use the Intermediate Value Theorem to determine where there

Use the Intermediate Value Theorem to determine where there is a real zero of the following function.

f(x) = x^3 + 5x^2 - 100

Choose one of the following:

a)f has a zero between 0 and 1.

b)f has a zero between 1 and 2.

c)f has a zero between 2 and 3.

d)f has a zero between 3 and 4.

e)f has a zero between 4 and 5.

f)f has a zero between 5 and 6.

g)f has a zero between 6 and 7.

h)f has a zero between 7 and 8.

f(x) = x^3 + 5x^2 - 100

Check f(x) at x= 0,1 ,2,3,----- 7,8

f(0) = -100 ; f(1) =1+5-100 =-96

f(1) = -96 ; f(2) = 8 + 20 -100 = -72

f(3) = 27 +45 -100 = 72 -100 = -28

f(4) = 44

So, f(3) = -28 i.e. it is -ve and f(4) =44 ie.e it is +ve .So,it means

that f(x) crosses x axis between x= 3 and x=4

So, there is a real root between x=3 and x=4

Option d)