Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Applications of Derivatives

Question:

The function $f(x)= 2x^3-3x^2-12x+4$ has :

Options:

two points of local maximum

two points of local minimum

one maximum and one minimum

no maximum and no minimum

Correct Answer:

one maximum and one minimum

Explanation:

The correct answer is option (3) → one maximum and one minimum

$f(x)= 2x^3-3x^2-12x+4$

$f'(x)= 6x^2-6x-12=0$

$x^2-x-2=0$

$⇒x=-1,2$

$f''(x)=12x-6$

$f''(-1)=-18$ point of maxima

$f''(2)=18$ point of minima