Application of Derivatives questions
910 published questions with worked solutions.
- The value of c in Lagrange's theorem for the function |x| in the interval [-1, 1] is
- The equation x + x x = 0 has at least one root in the interval
- If 4a + 2b + c = 0 then the equation 3ax^2 + 2bx + c = 0 has at least one real root lying between
- If the equation a_n x^n + a_ n-1 x^ n-1 + + a_1 x = 0, a_1 0, n 2, has a positive root then the equation na_n x^ n-1 + (n-1)a_...
- Let h(x) = f(x) - f(x) ^2 + f(x) ^3 for all real values of x. Then
- If f(x) = x, - /2 x /2, then
- Let f(x) = 2 ^3 x - 3 ^2 x + 12 x + 5, 0 x /2. Then f(x) is
- Let f(x) = -2x^3 + 21x^2 - 60x + 41. Then
- Let f(x) = x^2 + 1 [x] , 1 x 3.9. [ ] denotes the greatest integer function. Then
- Let f(x) = |x^2 - 3x - 4|, -1 x 4. Then
- Let f(x) = (2 - x) + (x) and ''(x) < 0 for x [0, 2]. Then
- Let f'(x) > 0 and g'(x) < 0 for all x R. Then
- Let f(x) = 2x^2 - |x|, x 0. Then f(x) is
- Let f(x) = x^3 - 6x^2 + 15x + 3. Then
- Let f(x) = a_5x^5 + a_4x^4 + a_3x^3 + a_2x^2 + a_1x, where a_i's are real and f(x) = 0 has a positive root _0. Then
- If f(x) satisfies the conditions of Rolle's theorem in [1,2] then _1^2f'(x) ,dx is equal to
- The function f(x)= _ -1 ^ x t(e^t-1)(t-2)^3(t-3)^5 ,dt has a local minimum at x which is equal to
- If (x)= _x^ x^2 (t-1) ,dt, 1 x 2, then the greatest value of (x) is
- Let f(x) be a function defined by f(x)= _1^x x(x^2-3x+2) ,dx, 1 x 3. Then the range of f(x) is
- Let f(x)=ax^3+bx^2+cx have relative extrema x=1 and at x=5. If _ -1 ^ 1 f(x) ,dx=6 then
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