Consider the function $f (x) = 8x^2 - 7x + 5$ on the interval $[-6, 6]$. The value of $c$ that satisfies the conclusion of the mean value theorem, is
$- 7/8$
$-4$
$7/8$
$0$
Verify Rolle's theorem for the function $y=x^{2}+2, a=-2$ and $b=2$
If $g(x) = 2f (2x^3 - 3x^2) + f(6x^2 - 4x^3 - 3)$, $\forall x \in R$ and $f"(x) > 0, \forall x \in R$ , then $g'(x) > 0$ for $x$ belonging to
The function $f(x) = x(x + 3){e^{ - (1/2)x}}$ satisfies all the conditions of Rolle's theorem in $ [-3, 0]$. The value of $c$ is
Examine if Rolle's Theorem is applicable to any of the following functions. Can you say some thing about the converse of Roller's Theorem from these examples?
$f(x)=x^{2}-1$ for $x \in[1,2]$
If the function $f(x) = 2x^2 + 3x + 5$ satisfies $LMVT$ at $x = 3$ on the closed interval $[1, a]$ then the value of $a$ is equal to