The sum of the maximum and minimum values of the function f(x)=|5 x-7|+[x2+. 2 x] is the interval [(5/4), 2], where [t] is the greatest integer ≤ t is

Question

The sum of the maximum and minimum values of the function f(x)=|5 x-7|+[x2+. 2 x] is the interval [(5/4), 2], where [t] is the greatest integer ≤ t is  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Graph of x2+2 x

Graph of | 5x - 7|

. f ( x )| min =4+0=4, at x=(7/5) . f ( x )| max =8+3=11, at x =2 Required sum =15

Q. The sum of the maximum and minimum values of the function $f (x) = ∣5 x - 7∣ + [x^{2} +$ $2 x]$ is the interval $[\frac{5}{4}, 2]$ , where $[t]$ is the greatest integer $\leq t$ is ______

Graph of $x^{2} + 2 x$

Graph of $∣5 x - 7∣$

$f (x) ∣_{m i n} = 4 + 0 = 4$ , at $x = \frac{7}{5}$
$f (x) ∣_{m a x} = 8 + 3 = 11$ , at $x = 2$
Required sum $= 15$

Q. The sum of the maximum and minimum values of the function f(x)=∣5x−7∣+[x2+ 2x] is the interval [45​,2], where [t] is the greatest integer ≤t is ______

Graph of x2+2x Graph of ∣5x−7∣ f(x)∣min​=4+0=4, at x=57​ f(x)∣max​=8+3=11, at x=2 Required sum =15

Q. The sum of the maximum and minimum values of the function $f (x) = ∣5 x - 7∣ + [x^{2} +$ $2 x]$ is the interval $[\frac{5}{4}, 2]$ , where $[t]$ is the greatest integer $\leq t$ is ______

Graph of $x^{2} + 2 x$

Graph of $∣5 x - 7∣$

$f (x) ∣_{m i n} = 4 + 0 = 4$ , at $x = \frac{7}{5}$
$f (x) ∣_{m a x} = 8 + 3 = 11$ , at $x = 2$
Required sum $= 15$