Let $f$ be differentiable for all$x$. If $f(1) = - 2$ and $f^{'}(x) \geq 2$ for $x \in \lbrack 1,\ 6\rbrack$, then

Question

Dr. Abubacker · Accepted Answer

(d)
Since, $\frac{f(6) - f(1)}{6 - 1} \geq 2$ $\left\lbrack \because\ \ \ f^{'}(x) = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \right\rbrack$
$\Rightarrow \ \ \ f(6) - f(1) \geq 10$
$\Rightarrow f(6) + 2 \geq 10$
$\Rightarrow \ \ f(6) \geq 8$

Q. Let $f$ be differentiable for all$x$. If $f(1) = - 2$ and $f^{'}(x) \geq 2$ for $x \in \lbrack 1,\ 6\rbrack$, then

Explanation

Reviewed by Dr. Abubacker

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