then the value of is ________.
A curve passes through the point . Let the slope of the curve at each point. Then the equation of the curve is
At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by If the firm employs 25 more workers, then the new level of production of items is :
Let , where f’(x) denotes and g(x) is a given non − constant differentiable function on R with g(0) = g(2) = 0. Then the value of y(2) is
Let f be a real − value differentiable function on R (the set of all real numbers) such that f(1) = 1. If the y-intercept of the tangent at may point P(x, y) on the curve y = f(x) is equal to the cube of the abscissa of P, then the value of f(−3) is equal to
Match the statements / expressions in Column I with the open intervals in Column II
|Column I||Column II|
|(A)||Interval contained in the domain of definition of non- zero solutions of the differential equation||(p)|
Interval containing the value of the integral
|(C)||Interval in which at least one of the points of local maximum of||(r)|
|(D)||Interval in which is increasing||(s)|
If a tangent drawn to the curve y = f(x) at P(x, y) cuts the x-axis and the y-axis at A and B such that BP:AP = 3:1, given that f(1) = 1, then the
If the length of a tangent at any point on the curve y = f(x) intercepted between the point and the x-axis is of length 1, then what is the equation of the curve.