MHT CET202314 May 2023Evening ShiftMathematicsApplication of DerivativesActual

The function f (x)=x^3-6 x^2+9 x+2 has maximum value when x is

Options

Correct answer

A. 1

Step-by-step solution

aligned & f (x)=x^3-6 x^2+9 x+2 & f ^ (x)=3 x^2-12 x+9 aligned For maximum or minimum, aligned & f ^ (x)=0 & 3 x^2-12 x+9=0 & 3(x-1)(x-3)=0 & x=1,3 aligned Now, f ^ (x)=6 x-12 f ^ (1)=-6 < 0 f (x) is maximum at x=1 .

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 2025 The 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 2025 If f(x)=x e^ x(1-x) , x R , then f(x) is 2025 The angle between the curves y ^2= x and x ^2= y at the point (1,1) is 2025 If 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 = 2025 If the function f(x)= x- ^2 x is defined on the interval [- , ] , then f is strictly increasing in the interval 2025 If 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 = 2025 If 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 MHT CET PYQs