Engineering Mat...

The maximum value of the function \(f\left( x \right) = - \frac{5}{3}{x^3} + 10{x^2} - 15x + 16\) in the interval (0.5, 3.5) is 

If \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {1 + x}&{if\;x < 0}\\ {\left( {1 - x} \right)\left( {px + q} \right)}&{if\;x \ge 0} \end{array}} \right.\) satisfies the assumptions of Rolle’s Theorem in the interval [-1, 1], the ordered pair (p, q) is

Find C of Cauchy’s mean value theorem for the function 1/x and 1/x² in [4, 6]

If \(x = \mathop \sum \limits_{k = 1}^\infty {a_k}\sin kx\), for -π ≤ x ≤ π, the value of a₂ is ______

Consider the function f(x, y) = 2x² - 2x²y + y². Which of the following statement is true?

1. (0, 0) is minima
2. (1, 1) is saddle point
3. (-1, 1) is saddle point

If \(f\left( x \right) = {x^3} - 3x - 1\) is continuous in the closed interval \(\left[ {\frac{{13}}{7}, - \frac{{11}}{7}} \right]\) and f’(x) exists in the open interval \(\left( {\frac{{13}}{7}, - \frac{{11}}{7}} \right)\) then find the value of c such that it lies in \(\left( {\frac{{13}}{7}, - \frac{{11}}{7}} \right)?\)

The equation 2x − 1 − sin x = 0 has

The half range Fourier cosine series of the function \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}{x,\;\;\;0 < x < \frac{\pi }{2}}\\{\pi - x,\;\;\;\frac{\pi }{2} < x < \pi }\end{array}} \right.\) is given by