- Home
- Standard 12
- Mathematics
5. Continuity and Differentiation
medium
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
A
$3$
B
$4$
C
$5$
D
$1$
Solution
$f'\left( 3 \right) = \frac{{f\left( a \right) – f\left( 1 \right)}}{{a – 1}}$
$ \Rightarrow \frac{{2{a^2} + 3a – 5}}{{a – 1}} = 15$
$ \Rightarrow {a^2} – 6a + 5 = 0 \Rightarrow a = 5$
Standard 12
Mathematics
Similar Questions
hard