Question
What is the largest open interval on which f(x) = x² − 2x is strictly decreasing?
The correct answer is
(−∞, 1)
\(f\prime(x)=2x-2\lt 0\Leftrightarrow x\lt 1\Rightarrow(-\infty,1)\)
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Important Questions from Applications of Derivatives
What is the slope of the tangent of y = cos -1 (cos x) at x = \(-\frac{\pi}{5}\) ?
The maximum value of \(\sin \left( {{\rm{x}} + \frac{{\rm{\pi }}}{6}} \right) + \cos \left( {{\rm{x}} + \frac{{\rm{\pi }}}{6}} \right)\) in the interval \(\left( {0,\frac{{\rm{\pi }}}{2}} \right)\) is attained at
The derivative of the function y = 3|x| + 1 at the point x = 0 is
Given that f(x) = x 1/x , x > 0 has the maximum value at x = e, then
What is the minimum value of [x(x – 1) + 1] 1/3 , where 0 ≤ x ≤ 1?
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