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.

Suppose \(f(x)\) is a function such that \(y=f'(x)\) is given by the curve in the above diagram. If \(y= f'(x) \) is tangent to the \(x\)-axis at \(x=a=7,\) which of the following statements is NOT correct about \(f(x)?\)

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 such that the graph of \(y=f'(x)\) is as shown in the above diagram. If \[a = 2, b = 3, c = 5, d= 7,\]
and \(f'(e) = f'(d) \) for all \(e \geq d,\) which of following statements is correct?

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 function such that the graph of \(y=f'(x)\) is a line as shown in the above diagram. If \(a=19,\) which of following statements is correct?

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 function such that \(f'(x) = K(x-a)(x-b) ,\) where \(K\) is a positive constant. If \(a=5\) and \(b=10,\) which of following statements is NOT correct?

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!