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Calculus

Differentiability

Characteristics of graphs of f and f'

         

Given \(f'(x) = x^2 + 9x + k,\) if \(f(x)\) is an increasing function for all values of \(x,\) what is the range of \(k?\)

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 \(f(x)?\)

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?

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?

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?

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