Suppose \( f \) and \( g \) are differentiable functions on the interval \( [ 8 , 42 ] \) such that \( f \left( 8\right) = g \left( 8\right) \) and \( f' \left( x \right) < g' \left( x \right) \) for all \( x \) on \( ( 8 , 42 ) .\) If \( f \left( 42\right) = 48 \) , which of the following values NOT possible for \( g \left( 42\right)? \)

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!

Suppose \(f(x)\) is a differentiable function on the interval \( \left [6, 9 \right ]\) such that \(f(6) = 18\) and \(f(9) = 27 .\) Which of the following values must be contained in \( f'(\left [6, 9 \right ])?\)

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!

Suppose \(f(x) \) is a differentiable function on \(\left [ 6, 13 \right ] \) such that \( (2x-19)(f(x)-6) \neq f'(x)(x^2 - 19x + 78)\) for any \(x \in \left [ 6, 13 \right ]. \) Which of the following values must be contained in \(f(\left [ 6, 13 \right ])?\)

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!