Calculus (basic derivatives & tangent lines) Sept 2020

Find the derivative of the given equation
 $f\left(x\right)=\frac{1}{x^2}$ . Hint: Rewrite with a negative exponent first! 

•  $f'\left(x\right)=\frac{1}{2x}$  

•  $f'\left(x\right)=-2x^3$  

•  $f'\left(x\right)=2x$  

•  $f'\left(x\right)=-\frac{2}{x^3}$  

Differentiate h(x) = 3x^5/3 - 6x^1/6 + 3x

• h'(x) = 5x^2/3 - x^-5/6 + 3

• h'(x) = 3x^2/3 - 6x + 3

• h'(x) = 5x^4/3 - 6x + 3

• h'(x) = 3x^4/3 - x^-5/6 + 3

Tags

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

Find the slope of f(x) = -3x²-6x at x = 1.

• m = 0
• f'(x) = -6x - 6
• f'(x) = 6x
• m = -12

Which graph is the derivative of the top graph?

• A
• B
• C
• D

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What is the derivative of y = 2π?

• 0

• 2

• -2

• None of the above

Find the derivative of y = 2x² (3x - 4)

Hint: Do basic algebra first

• 6x³ - 8x²

• 18x² - 16x

• 15x² - 6x

• 6x - 4

At which point(s) are the slopes of the tangent lines zero (where are there horizontal tangent lines)?

• at C only

• at points A, C and E only

• at point B and D only

• at points A and E only

Tags

CCSS.HSF-IF.C.7D

For what value(s) of x is the function continuous but not differentiable?

• x = -1

• x = 0

• x = 2

• x = 3; x = -2

What is the equation of the line tangent to f(x)= 4x²+2x-1 at (0,-1)?

• y+1=2(x+1)

• y+1=2(x-0)

• y-1=2(x-0)

• y-0= -x-1

Find the equation of the tangent line at the point (-1,1) of: $f\left(x\right)\ =\ x^4$  

•  $y=-\frac{1}{4}x-3$  

•  $y=-4x-3$  

•  $y=\frac{1}{4}x+3$  

•  $y=4x+3$  

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7