JEE Main 2022 · 25 Jul · Shift 2 · Mathematics Q24

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MathematicsInteger+4 / -1Question 24 of 90

The sum of the maximum and minimum values of the function $f(x)=|5x-7|+\left[x^2+2x\right]$ in the interval $\left[\dfrac54,2\right]$ , where $[t]$ is the greatest integer $\le t$ , is ______.

Your answer

Answer and worked solution

Official answer: 15

On $\left[\frac54,2\right]$ $x^2+2x$ runs from $\frac{65}{16}$ to 8. Maximum at $x=2$ : $3+8=11$ . Minimum near $x=\frac75$ : $0+4=4$ (the floor is 4 there).

Sum 15.

Answer: 15

Topics:Maxima and minima Graphs of functions

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JEE Main 2022 · 25 Jul · Shift 2, Mathematics question 24