Application of Derivatives questions
910 published questions with worked solutions.
- The rate of change of the volume of a sphere with respect to its surface area, when its radius is 2 cm, is _____ cm ^3/ cm ^2
- If f(x) = a x + b x c x + d x is decreasing for all x, then
- If y=a x+bx^2+x has its extremum values at x = -1 and x = 2 then
- The maximum value of ( _1) ( _2) ( _n) under the constraints 0 _1, _2, , _n 2 and ( _1) ( _2) ( _n)=1 is
- The abscissa of the point on the curve y=a (e^ xa +e^ - xa ) where the tangent is parallel to the X -axis is
- If the line y = 4x - 5 is tangent to the curve y^2 = ax^3 + b at the point (2,3), then the value of 7a - 2b is...
- The equation of the tangent to the curve y = 9 - 3x^2 at the point where the ordinate and abscissa equal is...
- The coordinates of the points on the curve 4y = x^2 that are nearest to the point (0,5) are ...
- The derivative of the function f(x)= ^4x+ ^4x, 0 x 2 is positive for
- The number 28 is divided into two positive parts such that the sum of the cube of one part and the square of the other part is...
- If f(x)= (1+x)- x 1+x , then the values of x for which f(x) is monotonically increasing and monotonically decreasing are...
- If the function f(x)=ax^2+bx+ x satisfies all the conditions of Rolle's theorem on [0, ] and the slope of the tangent to the...
- Let g(x)=f(x)+f(1-x) and f''(x)<0, 0 x 1. then ...
- If the side of an equilateral triangle increases at the rate of 3 cm/sec, then the rate of change of increase of its area when...
- If the tangent to the curve xy+ax+by=0 at (1, 1) makes an angle of ^ -1 2 with positive direction of the x-axis, then the value...
- If the line x+By+C=0 is the normal to the curve given by x=a ^3t, y=b ^3t, ( where a,b 0) at a point t= 2 , then B - C =
- The equation of tangent to the curve y = (x + y) where -2 x 2 and which is parallel to the line x + 2y = 0, is
- If two curves x^2 - 4y^2 = 2 and 8x^2 = 40 - my^2 are orthogonal to each other then m =
- A normal is drawn at a point P(x, y) of a curve y = f(x). The normal meets the X axis at Q. l(PQ) = k. (k is a constant) Then...
- A population p(t) of 1000 bacteria introduced into a nutrient medium grows according to the relation p(t)=1000+ 1000t 100+t^2 ....
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