Find the slope of the tangent to the curves at the respective given points.
x = a cos³ t, y = b sin³ t at t = \(\frac { \pi }{ 2 } \)

Find the point on the curve y = x² − 5x + 4 at which the tangent is parallel to the line 3x + y = 7.

A truck travels on a toll road with a speed limit of 80 km/hr. The truck completes a 164 km journey in 2 hours. At the end of the toll road the trucker is issued with a speed violation ticket. Justify this using the Mean Value Theorem.

Suppose f(x) is a differentiable function for all x with f'(x) ≤ 29 and f(2) = 17. What is the maximum value of f(7)?

Explain why Rolle’s theorem is not applicable to the following functions in the respective intervals.
\(f(x)=|\frac{1}{x}|, x\in [-1,1]\)