DerivativesMedium
Second Derivative of x⁴
Differentiate twice to find the second derivative of a power function.
Method: Apply the power rule twice
Step-by-step solution
- 1
Find the first derivative
Apply the power rule to x⁴.
- 2
Differentiate again
Apply the power rule to 4x³.
- 3
Interpret
The second derivative describes how the first derivative changes and is nonnegative here.
Final answer
For x not equal to zero the function is concave up; at zero the second derivative is zero but concavity does not switch.
Common mistake
The notation d²/dx² means two successive derivatives, not squaring the first derivative.
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