Question

The slope of the tangent to the curves x = 4t³ + 5, y = t² - 3 at t = 1 is ______

Options

• 0

• `1/6`

• 1

• -6

Answer 1

The slope of the tangent to the curves x = 4t³ + 5, y = t² - 3 at t = 1 is `underline(1/6)`.

Explanation:

x = 4t³ + 5, y = t² - 3

∴ `dx/dt = 12t^2, dy/dt = 2t`

∴ `dy/dx = (dy/dt)/(dx/dt) = (2t)/(12t^2) = 1/(6t)`

∴ `(dy/dx)_(t = 1) = 1/6`