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

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