State Rolle's Theorem and show that x3 + 3x + 1 = 0 has exactly one re | Basic Mathematics 2080

Basic Mathematics208010 marksNumerical: Rolle's theorem and areaRolle's theorem

State Rolle's Theorem and show that $x^3 + 3x + 1 = 0$ has exactly one real solution. Find the area of the region enclosed by the parabola $y = 2 - x^2$ and the line y = -x. [5+5]

Function/equation: $x^3 + 3x + 1 = 0$ If a function $f$ is: 1. continuous on the closed interval $[a, b]$ , 2. differentiable on the open interval $(a, b)$ , and 3. $f(a) = f(b)$ , then there exists at least one point $c \in (a, b)$ such that $f'(c) = 0$ . Let $f(x) = x^3 + 3x + 1$ . This is a polyn...

Function/equation: $x^3 + 3x + 1 = 0$ If a function $f$ is: 1. continuous on the closed interval $[a, b]$, 2. differentiable on the open interval $(a, b)$, and 3. $f(a) = f(b)$, then there exists at least one point $c \in (a, b)$ such that $f'(c) = 0$. Let $f(x) = x^3 + 3x + 1$. This is a polyn...

← PreviousAll questions Next question →

Up nextDefine absolute value function and Sketch the graph of absolute value.

State Rolle's Theorem and show that x3 + 3x + 1 = 0 has exactly one real solution. Find the area of the region enclosed by the parabola y = 2 - x2 and the line y = -x. [5+5]