AI Calculus Practice

Find the derivative of the given equation
f(x) = x³ + x² + 3

• 3x² + 2x
• 3x + 2x 
• 3x + 2x + 3
• x³ + x² 

What is f'(1) if f(x) = -3x²-6x.

• 0

• -6x - 6

• 6x

• -12

Find the derivative of the given equation
f(x) = 7

• 7
• 0
• 7x
• 14

Find the derivative of y = 5x⁴

• (5x³)/4
• 20x⁴
• 20x³
• x⁵

Find the derivative of f(x) = 6x³⁰ -2x¹⁵ + 4x³ - 2x + 1

• f'(x) = 18x²⁹ + 30x¹⁵ + 12x³ 
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² 
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² - 2
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² +1

At which point(s) will the f'(x)=0?

• at C only

• at points A, C and E only

• at point B and D only

• at points A and E only

Find the derivative of the given equation
f(x) = -4x

• 4
• x
• -4
• 0

Find f '(2)  if
f(x) = x² + 2x

• 2x + 2
• 6
• 12
• 2x

Find the derivative of the given equation
f(x) = 1 - x²

• 1 - 2x
• -2x
• -2
• -1

Where on this graph would you find an instantaneous rate of change of 0?

• x = -3

• x = 0

• x = 3

• x is approximately -4.8 and x=0

• None