3.6 Equations of Tangent Lines

Authored by Sumer Wong

Mathematics

9th - 12th Grade

CCSS covered

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

When we "take the derivative" of a function what are we finding?

What's a derivative?

The rate at which our struggles in Calculus are increasing.

The slope of the secant line

The slope of the tangent line

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Point-Slope Form is

$y-y_1=m\left(x-x_1\right)$

$y_1-y=m\left(x_1-x\right)$

$y=mx+b$

None of the above

What is the derivative of $f\left(x\right)=9x^2-8x+5$

$f'\left(x\right)=18x-8$

$f'\left(x\right)=29x-8$

$f'\left(x\right)=18x-8x$

$f'\left(x\right)=9x^3-8x^2+5$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of $f\left(x\right)=3x^7+5x^4+2x^3+7x+1$

$f'\left(x\right)=21x^6+20x^3+6x^2+7$

$f'\left(x\right)=21x^7+20x^4+6x^3+7x$

$f'\left(x\right)=21x^7+20x^4+6x^3+7x+1$

$f'\left(x\right)=21x^8+20x^6+6x^5+7x^2$

FILL IN THE BLANKS QUESTION

30 sec • 1 pt

Find the slope at x = 7 of the equation f(x) = 3x²

(a)

What is the slope of the tangent line when x = 5 for $f\left(x\right)=9x^2-8x+5$

(a)

FILL IN THE BLANKS QUESTION

30 sec • 1 pt

What is the slope of the tangent line at (1, 3) for $f\left(x\right)=4x^2+7x-8$

(a)

FILL IN THE BLANKS QUESTION

30 sec • 1 pt

What is the equation for the tangent line at (1, 3) for $f\left(x\right)=4x^2+7x-8$

(a)

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3.6 Equations of Tangent Lines

When we "take the derivative" of a function what are we finding?

Point-Slope Form is

What is the derivative of f(x)=9x2−8x+5f\left(x\right)=9x^2-8x+5f(x)=9x2−8x+5

What is the derivative of f(x)=3x7+5x4+2x3+7x+1f\left(x\right)=3x^7+5x^4+2x^3+7x+1f(x)=3x7+5x4+2x3+7x+1

Find the slope at x = 7 of the equation f(x) = 3x2 (a)

What is the slope of the tangent line when x = 5 for f(x)=9x2−8x+5f\left(x\right)=9x^2-8x+5f(x)=9x2−8x+5 (a)

What is the slope of the tangent line at (1, 3) for f(x)=4x2+7x−8f\left(x\right)=4x^2+7x-8f(x)=4x2+7x−8 (a)

What is the equation for the tangent line at (1, 3) for f(x)=4x2+7x−8f\left(x\right)=4x^2+7x-8f(x)=4x2+7x−8 (a)

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What is the derivative of $f\left(x\right)=9x^2-8x+5$

What is the derivative of $f\left(x\right)=3x^7+5x^4+2x^3+7x+1$

Find the slope at x = 7 of the equation f(x) = 3x²

(a)

What is the slope of the tangent line when x = 5 for $f\left(x\right)=9x^2-8x+5$

(a)

What is the slope of the tangent line at (1, 3) for $f\left(x\right)=4x^2+7x-8$

(a)

What is the equation for the tangent line at (1, 3) for $f\left(x\right)=4x^2+7x-8$

(a)