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Tangent lines practice problems

The equation of the line tangent to a curve at a point. 30 problems with worked solutions; in 30 of them every equation is proved by a computer algebra system.

Find an equation of the tangent line to \( \displaystyle y = - 3 x^{3} + x^{2} + 3 x - 1 \) at \( \displaystyle x = 2 \).

Problem 2.729easy✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = - 3 x^{3} + 2 x^{2} - 2 x - 3 \) at \( \displaystyle x = 4 \).

Problem 2.775easy✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = 2 x^{3} - 2 x^{2} - x - 3 \) at \( \displaystyle x = -1 \).

Problem 2.777easy✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = 2 x + \sin{\left(x \right)} \) at \( \displaystyle x = \pi \).

Problem 2.725medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = x e^{2 x} \) at \( \displaystyle x = 2 \).

Problem 2.726medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = x e^{2 x} \) at \( \displaystyle x = 1 \).

Problem 2.727medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = - x - 2 \sin{\left(x \right)} + 2 \) at \( \displaystyle x = \pi \).

Problem 2.728medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = x + \sin{\left(x \right)} \) at \( \displaystyle x = \frac{\pi}{2} \).

Problem 2.730medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = x e^{- x} \) at \( \displaystyle x = -1 \).

Problem 2.731medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = x e^{2 x} \) at \( \displaystyle x = -1 \).

Problem 2.732medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = - 2 x^{2} + x + 3 - \frac{3}{x} \) at \( \displaystyle x = -1 \).

Problem 2.733medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = x e^{- 2 x} \) at \( \displaystyle x = -1 \).

Problem 2.734medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = x e^{2 x} \) at \( \displaystyle x = 4 \).

Problem 2.735medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = 2 \sqrt{x} + x - 3 \) at \( \displaystyle x = 9 \).

Problem 2.736medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = 2 \sqrt{x} + 2 x + 2 \) at \( \displaystyle x = 4 \).

Problem 2.737medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = - x + 3 \sin{\left(x \right)} \) at \( \displaystyle x = \pi \).

Problem 2.738medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = - 3 x^{2} - 4 x - 2 + \frac{2}{x} \) at \( \displaystyle x = -1 \).

Problem 2.739medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = 2 \sqrt{x} - 3 x - 2 \) at \( \displaystyle x = 1 \).

Problem 2.770medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = \sqrt{x} - 2 x + 1 \) at \( \displaystyle x = 4 \).

Problem 2.771medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = - x^{2} - 2 x - 4 - \frac{3}{x} \) at \( \displaystyle x = 2 \).

Problem 2.772medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = 3 x^{2} - 3 x + 2 + \frac{2}{x} \) at \( \displaystyle x = -1 \).

Problem 2.773medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = - 2 x^{2} + 2 x + 4 + \frac{2}{x} \) at \( \displaystyle x = 4 \).

Problem 2.774medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = x e^{x} \) at \( \displaystyle x = 4 \).

Problem 2.776medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = x e^{- 2 x} \) at \( \displaystyle x = 2 \).

Problem 2.778medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = - x - \sin{\left(x \right)} \) at \( \displaystyle x = 0 \).

Problem 2.779medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = - x^{2} + 3 x - 4 + \frac{1}{x} \) at \( \displaystyle x = 1 \).

Problem 2.780medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = 2 \sqrt{x} + 3 x + 2 \) at \( \displaystyle x = 4 \).

Problem 2.781medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = x e^{- 2 x} \) at \( \displaystyle x = 4 \).

Problem 2.782medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = - x + 2 \sin{\left(x \right)} \) at \( \displaystyle x = \pi \).

Problem 2.783medium✓ Every equation proved

Find an equation of the tangent line to \( \displaystyle y = - x + 2 \sin{\left(x \right)} \) at \( \displaystyle x = 0 \).

Problem 2.784medium✓ Every equation proved