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.
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.
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