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The derivative of $f(x) = x^3 + 2x^2 + 1$ at $x = 1$ is:
A$4$, since $f'(x) = 3x^2 + 2x$ at $x = 1$
B$3$, ignoring the linear term contribution at $x = 1$
C$5$, mistakenly counting the constant in differentiation
D$7$, since $f'(x) = 3x^2 + 4x$ gives $3 + 4 = 7$
Answer & Solution
Correct answer: D. $7$, since $f'(x) = 3x^2 + 4x$ gives $3 + 4 = 7$
$f'(x) = 3x^2 + 4x$; $f'(1) = 3 + 4 = 7$.
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