If R is the least value of a such that the function fx = x^2 + ax + 1 is increasing on [1,2] and S is the greatest value of a such that the function…

Question

If R is the least value of a such that the function fx = x^2 + ax + 1 is increasing on [1,2] and S is the greatest value of a such that the function f(x) = x^2 + ax + 1 is decreasing on [1, 2], then the value of |R-S| is

MARKS Content Team · Accepted Answer

Correct answer: 2. If f^(')(x)=2x+a≥0∀x∈[1,2] ⇒a≥-2x∀x∈[1,2] a_min=R=-2 If a_max=S=-4 |R-S|=2 Alternate : If f(x) is increasing for all x∈[1,2] then -a/2≤1⇒a≥-2⇒R=-2 If f(x) is decreasing for x∈[1,2], then -a/2≥2⇒a≤-4⇒S=-4 |R-S|=2

If $R$ is the least value of $a$ such that the function $f (x) = x^{2} + a x + 1$ is increasing on $[1, 2]$ and $S$ is the greatest value of $a$ such that the function $f (x) = x^{2} + a x + 1$ is decreasing on $[1, 2]$ , then the value of $| R - S |$ is

Solution

Relevant Questions

If R is the least value of a such that the function fx = x2 + ax + 1 is increasing on [1,2] and S is the greatest value of a such that the function f(x) = x2 + ax + 1 is decreasing on [1, 2], then the value of |R-S| is

Solution

Relevant Questions

If $R$ is the least value of $a$ such that the function $f (x) = x^{2} + a x + 1$ is increasing on $[1, 2]$ and $S$ is the greatest value of $a$ such that the function $f (x) = x^{2} + a x + 1$ is decreasing on $[1, 2]$ , then the value of $| R - S |$ is