Friday

July 25, 2014

July 25, 2014

Posted by **patel** on Saturday, September 22, 2012 at 11:57pm.

0.1 in [1, 2] containing a root of the equation. (Enter your answer using interval notation.)

x7 + 7x − 10 = 0

- calculus -
**Steve**, Sunday, September 23, 2012 at 7:40amf(1) = -2

f(2) = 134

so there is indeed at least one root in [1,2]

f'(x) = 7x^6 + 7

f'(x) > 0 everywhere, so f(x) is strictly increasing.

Since f(2) is so much greater than f(1), I'd expect to find the root near 1

f(1) = -2

f(1.05) = -1.243

f(1.10) = -0.352

f(1.15) = +0.710

so, there is a root in [1.05,1.15]

**Related Questions**

calculus - Find all values of x in the interval [0, 2π] that satisfy the ...

calculus - consider the equation below f(x)=e^(7x)+e^(-x) find the intervals on...

Algebra 2 help - Consider the following functions. f(x) = x2 − 3x, g(x...

Calculus Help Please!!! - Verify the given linear approximation at a = 0. Then ...

college algebra - Let f(x) = square root (x + 2) and g(x) = x^2 − 2. ...

Calculus Help - The formula C =5/9(F − 32), where F ≥ −459.67...

Calculus - Can someone help me finish this question... I got most of the ...

math - Find interval length 1/4 in [1,2] containing the root of the equation x^7...

Calculus - Answer the following questions for the function f(x) = sin^2(x/3) ...

Calculus Help Please!!! - Verify the given linear approximation at a = 0. Then ...