Maths · Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
The equation of tangent at those points where the curve meets -axis are
The equation of tangent at those points where the curve \( y=x^{2}-3 x+2 \) meets \( x \) -axis are
- A. \( x-y+2=0, x-y-1=0 \)
- B. \( x+y-1=0, x-y-2=0 \)
- C. \( x-y-1=0, x-y=0 \)
- D. \( x-y=0, x+y=0 \)
Step-by-step solution
The curve y = x^2 - 3x + 2 meets the x-axis (y=0) at points where x^2 - 3x + 2 = 0, giving x=1 and x=2. The derivative dy/dx = 2x - 3 gives slopes: at x=1, slope = -1; at x=2, slope = 1. Tangent equations: at (1,0), y - 0 = -1(x-1) ⇒ x+y-1=0; at (2,0), y - 0 = 1(x-2) ⇒ x-y-2=0.
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