Calculus & Vectors (MCV4U) · Derivatives and Their Applications

Equation of a tangent line

Find the equation of the tangent line to a polynomial curve at a given point. Unlimited questions, five difficulty levels, and a full worked solution every time — free.

Practice this skill Curriculum: MCV4U-DC1.6

Try one

Find the equation of the tangent line to f(x) at x = 3.

f(x) = −3x2 + 17x + 1
  • y = −x + 28
  • y = −6x + 43
  • y = −x + 1
  • y = −x + 22

Answer: y = -x + 28

See one solved, step by step

Find the equation of the tangent line to f(x) at x = -3.

f(x) = 2x2 + 15x + 3
  • y = 3x - 15
  • y = 4x - 12
  • y = 3x + 3
  • y = 3x - 33
📘 Worked solution
1f(−3) = −24Evaluate the function at x = -3 to get the point on the curve.
2f'(x) = 4x + 15Differentiate f(x) to get a formula for the slope of the tangent at any x.
3f'(−3) = 3Substitute x = -3 into f'(x) to get the actual slope at that point.
4y = 3x - 15Use point-slope form with slope 3 through (-3, -24), then simplify to y = mx + k.

Ready to master it?

Jump into unlimited practice — your Winny Score tracks you to 100. And if it won't click, a real tutor will make it click: first lesson free.

Start practicing