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Excel in math and science
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Differentiability
Those friendly functions that don't contain breaks, bends or cusps are "differentiable". Take their derivative, or just infer some facts about them from the Mean Value Theorem.
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
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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
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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
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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
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What is the value of \(\displaystyle{\lim_{x \rightarrow 0^{+} }\frac{e^{7\sin x}-e^{7x}}{\sin x - x} }?\)
Excel in math and science
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It's hard to learn from lectures and videos
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How many real solutions are there to the following equation: \[ \frac{4}{3}x^3 + 7x + 2=0? \]
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
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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 \(f(\left [ 6, 13 \right ])?\)