use the intermediate value theorem to show that there is a root of the given equation in the specified…

use the intermediate value theorem to show that there is a root of the given equation in the specified interval.\n( e ^ { x } = 5 - 4 x , quad ( 0,1 ) )\nthe equation ( e ^ { x } = 5 - 4 x ) is equivalent to the equation ( f ( x ) = e ^ { x } - 5 + 4 x = 0 ). ( f ( x ) ) is continuous on the interval ( 0,1 ). ( f ( 0 ) = ), and ( f ( 1 ) = ). since\n, there is a number ( c ) in ( ( 0,1 ) ) such that ( f ( c ) = 0 ) by the intermediate value theorem. thus, there is a root of the equation ( e ^ { x } = 5 - 4 x ), in the interval

use the intermediate value theorem to show that there is a root of the given equation in the specified interval.\n( e ^ { x } = 5 - 4 x , quad ( 0,1 ) )\nthe equation ( e ^ { x } = 5 - 4 x ) is equivalent to the equation ( f ( x ) = e ^ { x } - 5 + 4 x = 0 ). ( f ( x ) ) is continuous on the interval ( 0,1 ). ( f ( 0 ) = ), and ( f ( 1 ) = ). since\n, there is a number ( c ) in ( ( 0,1 ) ) such that ( f ( c ) = 0 ) by the intermediate value theorem. thus, there is a root of the equation ( e ^ { x } = 5 - 4 x ), in the interval

Answer

Explanation:

Step1: Calculate (f(1))

Given (f(x)=e^{x}-5 + 4x), substitute (x = 1) into (f(x)). [ \begin{align*} f(1)&=e^{1}-5+4\times1\ &=e - 5+4\ &=e-1 \end{align*} ] Since (e\approx2.718), then (f(1)=e - 1\approx2.718-1 = 1.718)

Answer:

(f(1)\approx1.718)