Mathematics Tes...

Given, f(x) = x³ – 12x² + 45x + 8. What is the minimum value of f(x)?

A particle is moving in a straight line and its distance x from a fixed point on the line at any time t seconds is given by, x = t⁴/12 – 2t³/3 + 3t²/2 + t + 15. At what time is the velocity minimum?

Given, f(x) = x³ – 12x² + 45x + 8. At which point does f(x) has its maximum?

Given, f(x) = x³ – 12x² + 45x + 8. At which point does f(x) has its minimum?

At which point does f(x) = |x – 1| has itslocal minimum?

A particle is moving in a straight line and its distance x from a fixed point on the line at any time t seconds is given by, x = t⁴/12 – 2t³/3 + 3t²/2 + t + 15. What is the minimum velocity?

What will be the equation of the normal to the parabola y² = 5x that makes an angle 45° with the x axis?

What will be the equation of the normal to the parabola y2 = 3x which is perpendicular to the line y = 2x + 4?

What will be the equation of the circle which touches the line x + 2y + 5 = 0 and passes through the point of intersection of the circle x² + y² = 1 and x² + y² + 2x + 4y + 1 = 0?

If the curves x2/a + y2/b = 1 and x2/c + y2/d = 1 intersect at right angles, then which one is the correct relation?