Curve Sketching

Concept Quizzes

Curve Sketching Warmup
Turning Points
Curve Sketching
Increasing / Decreasing Functions
Vertical Asymptotes
Relative Magnitude of Functions
Tangent to a Curve
Normal to a Curve

Challenge Quizzes

Curve Sketching: Level 3 Challenges
Curve Sketching: Level 4 Challenges

Tangent to a Curve

Suppose $y=f(x)$ is a curve such that the slope of the line tangent to the curve at an arbitrary point $(x, y)$ is given by $xe^{-x}.$ If $y=f(x)$ passes through the origin $(0, 0),$ what is the value of $f(18)?$

1 - \frac{22}{e^{18}}

1 - \frac{20}{e^{18}}

1 - \frac{21}{e^{18}}

1 - \frac{19}{e^{18}}

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by Brilliant Staff

If the tangent lines to the curve $y=2x^3+ax^2+bx+c$ at the two points $(1, 15)$ and $(2, 37)$ are parallel, what is $a+b+c?$

14 16 15 13

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What is the equation of the tangent line to the curve $y=5x^2-8x+1$ at the point $(4, 49)?$

y=32x-79

y=79x+32

y=32x+79

y=79x-32

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by Brilliant Staff

A curve $y=ax^2+bx+c$ passes through the point $(1, 18)$ and the tangent line at the point $(2, 27)$ has slope $1$ . What is the sum of the constants $a+b+c?$

18 14 16 20

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If the tangent line to the curve $f(x) = x^{3}+7$ at the point $(4, 71)$ is given by $y=px+q,$ what is $p+q?$

-73 -83 -68 -78

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by Brilliant Staff

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