Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KVPY2010MathematicsApplication of Derivatives

The figure shown below is the graph of the derivative of some function y=f^ (x) . Then-

Options

  1. Af has local minima at x=a, b and a local maximum at x=c
  2. Bf has local minima at x = b , c and a local maximum at x = a
  3. Cf has local minima at x = c , a and a local maximum at x = b
  4. Dthe given figure is insufficient to conclude any thing about the local minima and local maxima of f ,

Correct answer

C. f has local minima at x = c , a and a local maximum at x = b

Step-by-step solution

f ^ ( a )= f ^ ( b )= f ^ ( c )=0 . array l f ^ ( a ⁻ ) 0 f ^ ( c ⁻ ) 0 array ] minima at a & c . f ^ ( b ⁻ )>0 f ^ ( b ⁺ ) < 0 ] . at b

Practice Application of Derivatives on Quantrex Academy →

More from Application of Derivatives

Consider the quadratic equation a x^2+b x+c=0 , where 2 a+3 b+6 c=0 and let g(x)= a x^3 3 + b x^2 2 +c x . Statement-I : The given quadratic equation ax ^2+ bx + c =0 has at least 2025The difference between the absolute maximum and absolute minimum values of the function f(x)=2 x^3-15 x^2+36 x-30 on [-1,4] is 2025If f(x)=x e^ x(1-x) , x R , then f(x) is 2025The angle between the curves y ^2= x and x ^2= y at the point (1,1) is 2025If the tangent of the curve 4 y^3=3 a x^2+x^3 drawn at the point (a, a) forms a triangle of area 25 24 sq.units with the coordinate axes then a = 2025If the function f(x)= x- ^2 x is defined on the interval [- , ] , then f is strictly increasing in the interval 2025If the Lagrange's mean value theorem is applied to the function f(x)=e^x defined on the interval [1,2] and the value of c (1,2) is k , then e^ k-1 = 2025If the tangent to the curve x y+a x+b y=0 at (1,1) makes an angle Tan ⁻¹ 2 with X -axis, then ab a + b = 2025 Full Application of Derivatives list All KVPY PYQs