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Equation of a tangent line worksheets Grade 12

Find the equation of the tangent line at a point.

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How to do it

The slope is f′(a) and the point is (a, f(a)). Write y − f(a) = f′(a)(x − a), then solve for y.

f(x)=x3−6x+4at x=−2→y=6x+20f(x) = x^{3} - 6x + 4\quad \text{at }x = -2\quad \to \quad y = 6x + 20
f(−2)=(−2)3−6(−2)+4=8f(-2) = (-2)^{3} - 6(-2) + 4 = 8the point
f′(x)=3x2−6f'(x) = 3x^{2} - 6
f′(−2)=3(−2)2−6=6f'(-2) = 3(-2)^{2} - 6 = 6the slope
y−8=6(x+2)y - 8 = 6(x + 2)point-slope form
y=6x+20y = 6x + 20

Example problems

  1. f(x)=2x2−2at x=1→f(x) = 2x^{2} - 2\quad \text{at }x = 1\quad \to \quad
  2. f(x)=2x3−3x−1at x=3→f(x) = 2x^{3} - 3x - 1\quad \text{at }x = 3\quad \to \quad
  3. f(x)=−3x2−4x−4at x=0→f(x) = -3x^{2} - 4x - 4\quad \text{at }x = 0\quad \to \quad
  4. f(x)=−2x2+3x+9at x=1→f(x) = -2x^{2} + 3x + 9\quad \text{at }x = 1\quad \to \quad

Limits and derivatives

  1. Evaluating limits
  2. The power rule for derivatives
  3. The product rule
  4. The quotient rule
  5. The chain rule
  6. Derivatives of trig, exponential and log functions
  7. Equation of a tangent line
  8. Derivatives as rates of change
  9. Finding maximum and minimum points