Application of Derivatives questions
910 published questions with worked solutions.
- Let the normal at a point P on the curve y^2-3x^2+y+10=0 intersect the y-axis at (0, 3 2 ). If m is the slope of the tangent at P...
- The length of the perpendicular from the origin, on the normal to the curve, x^2+2xy-3y^2=0 at the point (2, 2) is :
- Let S be the set of all functions f : [0,1] → R, which are continuous on [0,1] and differentiable on (0, 1). Then for every f in...
- Let f(x) be a polynomial of degree 3 such that f(– 1) = 10, f(1) = – 6, f(x) has a critical point at x = – 1 and f '(x) has a...
- Let f : (–1, ∞) → R be defined by f(0) = 1 and f(x)= 1 x _e(1+x), x 0. Then the function f :
- The equation of the normal to the curve y=(1+x)^ 2y + ^2( ^ -1 x) at x = 0 is :
- If the function f(x) = ( 1x )^ 2x ; x > 0 attains the maximum value at x = 1e then:
- If the tangent to the curve y = x + sin y at a point (a, b) is parallel to the line joining (0, 3 2 ) and ( 1 2 ,2 ), then:
- Let P(h, k) be a point on the curve y = x² + 7x + 2, nearest to the line, y = 3x – 3. Then the equation of the normal to the...
- If p(x) be a polynomial of degree three that has a local maximum value 8 at x = 1 and a local minimum value 4 at x = 2; then p(0)...
- The function, f(x)=(3x-7)x^ 2/3 , x R, is increasing for all x lying in
- The number of critical points of the function f(x) = (x − 2)^ 2/3 (2x + 1) is:
- Let f(x) = 4cos³x + 3√3 sin²x − 10. The number of points of local maxima of f in interval (0, 2π) is:
- For the function f(x) = (cos x) − x + 1, x ∈ R, between the following two statements (S1) f(x) = 0 for only one value of x in [0,...
- If the function f(x) = 2x³ − 9ax² + 12a²x + 1, a > 0 has a local maximum at x = α and a local minimum x = α², then α and α² are...
- Let A be the region enclosed by the parabola y² = 2x and the line x = 24. Then the maximum area of the rectangle inscribed in the...
- The area (in sq. units) of the largest rectangle ABCD whose vertices A and B lie on the x-axis and vertices C and D lie on the...
- The minimum value of 2^ x +2^ x is :
- If the minimum and the maximum values of the function f: [ 4 , 2 ] R, defined by : f( )= vmatrix - ^2 &-1- ^2 &1 - ^2 &-1- ^2 &1...
- If x = 1 is a critical point of the function f(x)=(3x^2+ax-2-a)e^x, then :
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