Question:
For what value of \(x\), the function
\[
2x^3+3x^2-36x+10
\]
has minimum?
For what value of \(x\), the function
\[
2x^3+3x^2-36x+10
\]
has minimum?
Show Hint
For minimum, use \(f'(x)=0\) and check \(f''(x)>0\).
Updated On: May 7, 2026
- \(-2\)
- \(-3\)
- \(2\)
- \(3\)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Let: \[ f(x)=2x^3+3x^2-36x+10 \]
Step 2: Differentiate: \[ f'(x)=6x^2+6x-36 \] \[ f'(x)=6(x^2+x-6) \] \[ f'(x)=6(x+3)(x-2) \]
Step 3: Critical points: \[ x=-3,\quad x=2 \]
Step 4: Second derivative: \[ f''(x)=12x+6 \] At \(x=2\): \[ f''(2)=24+6=30>0 \]
Step 5: Since second derivative is positive, minimum occurs at: \[ x=2 \] \[ \boxed{2} \]
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