Question

show that the equation f(x)=x^2+6x-7 has at least one solution in the interval [-8,0].

Answer 1

use IVT

Answer 2

x^2 + 7x - x - 7
(x^2 - x) + (7x - 7)
x(x - 1) + 7(x - 1)
(x + 7)(x - 1) = 0;
x1 = -7; x2 = 1

Answer 3

Use Rolle's Theorem which says that if f(a)=f(b) where f(x) is continuous and differentiable in (a,b), f'(x) has atleast one root in the interval (a,b)
Integrate ur given function and label it F(x). Substitute 0 and 8 in F(x) and ull see that they give the same value. Hence the derivative of F(x), which we know is f(x), has atleast one solution in (0,8).