Application of Derivatives questions
910 published questions with worked solutions.
- The number of values of x where the function f(x) = x + ( 2 ,x) attains its maximum is
- The function f(x) = x 1 + x x has
- Let f(x) = e^x x be the equation of a curve. If at x = a, 0 a 2 , the slope of the tangent is the maximum then the value of a is
- Let the tangent to the graph of y = f(x) at the point x = a be parallel to the x-axis, and let f'(a-h) > 0 and f'(a+h) < 0, where...
- Let f(x) = x^3 + 3x^2 - 9x + 2. Then
- If f(x) = a _e|x| + bx^2 + x has extremums at x = 1 and x = 3 then
- The maximum value of ( 1x )^ 2x^2 is
- The maximum ordinate of a point on the graph of the function f(x) = x(1 + x) is
- If + = 3 then has a maximum value at =
- Let f(x) = x^3 - 6x^2 + 12x - 3. Then at x = 2, f(x) has
- Let f(x) = (x-p)^2 + (x-q)^2 + (x-r)^2. Then f(x) has a minimum at x = , where is equal to
- Let f(x) = ax + x^2. If it has a maximum at x = -3 then a is
- Let f(x) be a function such that f'(a) 0. Then at x = a, f(x)
- Let the function f(x) be defined as below. f(x) = cases ^ -1 + x^2, & 0 < x < 1 2x, & x 1 cases f(x) can have a minimum at x = 1...
- Let x be a number which exceeds its square by the greatest possible quantity. Then x is equal to
- The sum of two nonzero numbers is 8. The minimum value of the sum of their reciprocals is
- The point (0, 3) is nearest to the curve x^2 = 2y at
- If , be real numbers such that x^3 - x^2 + x - 6 = 0 has its roots real and positive then the minimum value of is
- Let f(x) = x + x^ -1 . Then
- Let f(x) = ax^3 + bx^2 + cx + 1 have extrema at x = , such that < 0 and f( ) f( ) < 0. Then the equation f(x) = 0 has
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