Application of Derivatives questions
910 published questions with worked solutions.
- If three positive real numbers a,b,c are in AP and abc=4, then the minimum possible value of b is
- If (0, 2 ), then x^2+x + ^2 x^2+x is always greater than or equal to
- If y=3^ x-1 +3^ -x-1 (x real), then the least value of y is
- If f(x)= ^2x+ ^2x, then
- If n_1,n_2,n_3, ,n_ 100 are positive real numbers such that n_1+n_2+n_3+ +n_ 100 =20 and k=n_1 (n_2+n_3+n_4 ) (n_5+n_6+ +n_9 )...
- 2^ +2^ is greater than
- Statement 1: If 3x+4y=5, then the greatest value of x^2y^3 is 3 16 . Statement 2: Greatest value occurs when 9x=8y.
- If 2p+3q+4r=15, then the maximum value of p^3q^5r^7 is
- The sixth term of an AP is equal to 2. The value of the common difference of the AP which makes the product T_1T_4T_5 least, is...
- If a_1,a_2,a_3 ,a_ 20 are AM's between 13 and 67, then the maximum value of a_1a_2a_3 a_ 20 is equal to
- The minimum value of the sum of real numbers a^ -5 ,a^ -4 ,3a^ -3 ,1,a^8 and a^ 10 with a>0 is
- If a,b,c,d are positive real numbers such that a+b+c+d=2, then M=(a+b)(c+d) satisfies the relation
- Let a,b,c and d be positive real numbers such that a+b+c+d=11. If the maximum value of a^5b^3c^2d is 3750 , then the value of is
- Let a_1,a_2,a_3, be an A.P. with a_6=2. Then the common difference of this A.P., which maximises the product a_1a_4a_5, is
- Let f:R R be such that for all x R, (2^ 1+x +2^ 1-x ), f(x) and (3^x+3^ -x ) are in A.P., then the minimum value of f(x) is
- The minimum value of f(x)=a^ a^x +a^ 1-a^x , where a,x R and a>0, is equal to
- If a_a is the greatest term in the sequence a_n= n^3 n^4+147 , n=1,2,3, , then a is equal to
- The minimum value of for which the equation 4 x + 1 1- x = has at least one solution in (0, 2 ) is
- Let f : (a,b) R be twice differentiable function such that f(x)= _a^xg(t)dt for a differentiable function g(x). If f(x) = 0 has...
- A wire of length 20 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a regular...
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