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Derivatives of Functions

Question 1 • AP Calculus AB - MA5186 A

Which statements are true about the function f(x) = 3x2 + 2? Check all that apply. f(h) = 9h + 2f(h) = 3h2 + 2 f(h) = 9h2 + 2f(x + h) = 3x2 + 3h2 + 2f(x + h) = 3x2 + 6xh + 3h2 + 2

Answer
A
f(h) = 9h + 2
B
f(h) = 3h2 + 2
C
f(h) = 9h2 + 2
D
f(x + h) = 3x2 + 3h2 + 2
E
f(x + h) = 3x2 + 6xh + 3h2 + 2

Explanation

Substitute h for x in f(x) = 3x² + 2 to get f(h) = 3h² + 2, so B is true. For f(x + h), substitute x + h and expand: 3(x + h)² + 2 = 3x² + 6xh + 3h² + 2, so E is true. The other expressions do not match these substitutions and expansions.

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