Application of Derivatives questions
910 published questions with worked solutions.
- Let C be the locus of the mirror image of a point on the parabola y^2=4x with respect to the line y = x. Then the equation of...
- Let f be a real valued function, defined on R – –1, 1 & given by f(x)=3 _e | x-1 x+1 |- 2 x-1 . Then in which of the following...
- The range of a∈R for which the function f(x) = (4a – 3)(x + _e5) + 2(a – 7) ( x 2 ) ^2 ( x 2 ), x 2n , n , has critical points,...
- If the normal to the curve y(x)= _0^x(2t^2-15t+10)dt at a point (a, b) is parallel to the line x + 3y = –5, a > 1, then the value...
- Consider the function f : R R defined by f(x)= (2- ( 1 x ) )|x|, x 0; 0, x=0 . Then f is :
- Let f : [–1, 1] R be defined as f(x) = ax^2+bx+c for all x [–1, 1], where a, b, c R such that f(–1) = 2, f'(–1) = 1 and for x...
- The minimum distance between any two points P_1 and P_2 while considering point P_1 on one circle and point P_2 on the other...
- Let P(x) be a real polynomial of degree 3 which vanishes at x = –3. Let P(x) have local minima at x = 1, local maxima at x = –1...
- The sum of all the local minimum values of the twice differentiable function f : R R defined by f(x)=x^3-3x^2- 3 2 f''(2)x+f''(1)...
- If the point on the curve y^2=6x, nearest to the point (3, 3 2 ) is ( , ), then 2( + ) is equal to _____.
- Let 'a' be a real number such that the function f(x)=ax^2+6x-15, x R is increasing in (- , 3 4 ) and decreasing in ( 3 4 , )....
- Let T be the tangent to the ellipse E:x^2+4y^2=5 at the point P(1, 1). If the area of the region bounded by the tangent T,...
- let f : R R be defined as f(x)= cases - 4 3 x^3+2x^2+3x, & x>0 3xe^x, & x 0 cases Then f is increasing function in the interval
- If P is a point on the parabola y = x^2 + 4 which is closest to the straight line y = 4x – 1, then the co-ordinates of P are :
- Let f:R R be defined as, f(x)= cases -55x, & x<-5 2x^3-3x^2-120x, & -5 x 4 2x^3-3x^2-36x-336, & x>4 cases Let A = x R: f is...
- For which of the following curves, the line x+ 3 y = 2 3 is the tangent at the point ( 3 3 2 , 1 2 )?
- If the curve y = ax^2 + bx + c, x , passes through the point (1, 2) and the tangent line to this curve at origin is y = x, then...
- If the tangent to the curve y = x^3 at the point P(t,t^3) meets the curve again at Q, then the ordinate of the point which...
- The function f(x)= 4x^3-3x^2 6 -2 x+(2x-1) x :
- The approximate value of (7.995)^ 1/3 correct to four decimal places is
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