Question

Find the slope of the tangent to the curves at the respective given points. 

(i) y = x⁴ + 2x² – x at x = 1 

(ii) x = a cos³t, y = b sin³t at t = π/2

Answer 1

(i) y = x⁴ + 2x² – x at x = 1 

The slope of the tangent at (x,y) is the value of (dy/dx) at (x₁,y₁) 

dy/dx = 4x³ + 4x - 1

dy/dx(at x = 1) = 4 + 4 - 1= 7

(i.e) slope of the tangent = 7

(ii) x = a cos³t, y = b sin³t 

Slope of the tangent = ∞