List of top Mathematics Questions on Maxima and Minima asked in CUET (UG)

Subject to constraints: 2x + 4y ≤ 8, 3x + y ≤ 6, x + y ≤ 4, x, y ≥ 0; The maximum value of Z = 3x + 15y is:

Let \( f(x) = x^3 - 6x^2 + 12x - 3 \), then at \( x = 2 \), \( f(x) \) has:

The maximum value of the function \(f(x)=x+\sqrt{1-x}\) on the interval [0,1] is, 

Match List I with List II

LIST I		LIST II
A.	The maximum value of the function \(f(x)=25x-\frac{5x^2}{2}+7\) in [-1,6] is	I.	24
B.	The minimum value of the function \(f(x)=2x^3-15x^2+36x+1\) in [1,5] is	II.	\(\frac{1}{16}\)
C.	The maximum value of the function \(f(x)=\frac{x}{2}-x^2\) in [0,1] is	III.	\(\frac{139}{2}\)
D.	The least value of the function \(f(x)=\frac{9}{x+3}+x\) in [-7,1], \(x\ne-3\) is	IV.	\(-\frac{37}{4}\)

Choose the correct answer from the options given below:

If $f(x)=ax^{2}+6x+5$ attains its maximum value at $x=1$, then the value of a is ________.