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Calculus

Differentiability

Concept Quizzes

Approximate Rate of Change
Slope of a Curve
Tangent Line at a Point
Local Linear Approximation
Intermediate Value Theorem
Mean Value Theorem
Rolle's Theorem
Characteristics of graphs of f and f'

Challenge Quizzes

Differentiability: Level 2 Challenges
Differentiability: Level 3 Challenges
Differentiability: Level 4 Challenges

Tangent Line at a Point

Which of the following is the tangent line to the curve $f(x)=2x^3-8x^2$ at the point $(1,-6)?$

y+10x=4

y-10x=4

y-10x=-4

y+10x=-4

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by Brilliant Staff

Find the equation of the tangent line to the curve $x^2y-x=4y^3-108$ for $x=0.$

108y-x=108

y-108x=324

y-108x=108

108y+x=324

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by Brilliant Staff

What is the equation of the line that passes through the point $(3,24)$ and is perpendicular to the tangent line of the curve $y=x^2+5x$ at that point?

y=\frac{1}{11}x + \frac{267}{11}

y=\frac{1}{11}x - \frac{267}{11}

y=-\frac{1}{11}x + \frac{267}{11}

y=-\frac{1}{11}x - \frac{267}{11}

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by Brilliant Staff

Given the curve $x=t^3, y=4t^2+9,$ what is the $y$ -intercept of the tangent line to the curve at $t=1 ?$

{31}

\displaystyle{ \frac{31}{3}}

-{31}

\displaystyle{ -\frac{31}{3}}

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What is the $y$ -intercept of the tangent line to the curve $y=e^{x-4}$ at the point $(5,e)?$

4e

-e

e

-4e

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