If the range of f x - x 2-7 x -60 in x -3-2- is - m - n - then the value of m - n is

Given polynomial nbsp; f(x)= x^2+7x+60 x coordinate of the vertex nbsp; b2a = nbsp; 7 2= 7 2 We know that nbsp; 72 2⇒ b2a 2 Now, ploting the graph ...

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Standard XII

Mathematics

Range of Quadratic Expression

If the range ...

Question

If the range of $f (x) = - x^{2} + 7 x + 60$ in $x \in [- 3, 2]$ is $[m, n]$ , then the value of $m + n$ is

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Solution

Given polynomial
$f (x) = - x^{2} + 7 x + 60$
$x -$ coordinate of the vertex
$- \frac{b}{2 a} = - \frac{7}{- 2} = \frac{7}{2}$
We know that
$\frac{7}{2} > 2 \Rightarrow - \frac{b}{2 a} > 2$

Now, ploting the graph of the polynomial, we get

Now,
$f (- 3) = - 9 - 21 + 60 = 30 f (2) = - 4 + 14 + 60 = 70$
Therefore, the range of the polynomial is
$[30, 70] ∴ m + n = 100$

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If the range of f(x)=−x2+7x+60 in x∈[−3,2] is [m,n], then the value of m+n is

Given polynomial f(x)=−x2+7x+60 x− coordinate of the vertex −b2a=−7−2=72 We know that 72>2⇒−b2a>2 Now, ploting the graph of the polynomial, we get Now, f(−3)=−9−21+60=30f(2)=−4+14+60=70 Therefore, the range of the polynomial is [30,70]∴m+n=100

If the range of $f (x) = - x^{2} + 7 x + 60$ in $x \in [- 3, 2]$ is $[m, n]$ , then the value of $m + n$ is