Question 11 Mark
Assertion (A): If x is real, then the minimum value of $x ^2-8 x +17$ is 1
Reason (R): If f"(x) > 0 at a critical point, then the value of the function at the critical point will be the minimum value of the function.
Reason (R): If f"(x) > 0 at a critical point, then the value of the function at the critical point will be the minimum value of the function.
Answer
View full question & answer→(a) Both A and R are true and R is the correct explanation of A.
Explanation: Let $f(x)=x^2-8 x+17$
$\therefore f^{\prime}(x)=2 x-8$
So, $f^{\prime}(x)=0$, gives $x=4$
Here $x=4$ is the critical number
Now, $f ^{\prime \prime}( x )=2;0, \forall x$
So, $x=4$ is the point of local minima.
$\therefore$ Minimum value of $f(x)$ at $x=4$,
$f(4)=4 \times 4-8 \times 4+17=1$
Hence, we can say that both Assertion and Reason are true and Reason is the correct explanation of the Assertion.
Explanation: Let $f(x)=x^2-8 x+17$
$\therefore f^{\prime}(x)=2 x-8$
So, $f^{\prime}(x)=0$, gives $x=4$
Here $x=4$ is the critical number
Now, $f ^{\prime \prime}( x )=2;0, \forall x$
So, $x=4$ is the point of local minima.
$\therefore$ Minimum value of $f(x)$ at $x=4$,
$f(4)=4 \times 4-8 \times 4+17=1$
Hence, we can say that both Assertion and Reason are true and Reason is the correct explanation of the Assertion.