Find intervals containing solutions to the following equations.

Question

Find intervals containing solutions to the following equations.
(a) f(x) = x − 3^−x = 0

b)f(x) = x^3 + 4.001x^2 + 4.002^x + 1.101 = 0.

I want help how can I find intervals and solutions for these function any hint about that
Thank you

Answer 1

(a) f(x) = x − 3^-x = 0.
Since f(0) = −1 and f(1) = 2/3
, by the intermediate value theorem,
there is some solution of f in the interval [0, 1].

 

(b) f(x) = x³ + 4.001x² + 4.002x + 1.101 = 0.
Since f(−3) = −1.896 and f(−2) = 1.101, by the intermediate value
theorem, there is some solution of f in the interval [−3, −2].

 

Could there have been a typo in part b) 4.002x not ^x. I have seen these problems before.

 

Consider graphing the functions to get an idea of the values to use to apply the intermediate value theorem.

 

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