Calculus Quiz 4-30-20

What is the equation of the line tangent to the curve y = x² at x = 1?

• y = 2x + 1

• y = 2x - 1

• y = -2x + 1

• y = x - 1

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

•  $y=-\frac{1}{4}x-3$  

•  $y=-4x-3$  

•  $y=\frac{1}{4}x+3$  

•  $y=4x+3$  

Find the equation of the NORMAL line at x = 0 if
 $f\left(x\right)\ =\ x^3+e^x$  

•  $y=-x+1$  

•  $y=\ x+1$  

•  $y=-x\ -1$  

•  $y=x\ -\ 1$  

What will be true at an inflection point? (select the best answer)

• f(x)=0

• f'(x)=0

• f''(x)=0

• The function is undefined

Find the intervals of concavity for

f(x) = x² + 2x + 1.

• concave up: (-∞,∞)

• concave down: (-∞,∞)

• concave up: (2, ∞)

  concave down: (-∞,2)

• concave up: (-∞,2)

  concave down: (2, ∞)

Over what interval(s) is f(x) concave up? (Be careful this is a graph of f')

• (-∞, -5) & (0, 2)

• (-3, 1)

• (-∞,-3) & (1, ∞)

• (-5, 0) & (2, ∞)

Identify the critical points of the following function:

g(x)=2x³-3x²

• x= -1 , 1

• x= 0

• x= 0, -1

• x= 0 , 1

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

Find the derivative
f(t) = (t² + 2t)⁵

• f'(t) = 5(2t+2)⁴
• f'(t) = 5(t² + 2t)⁴
•  f'(t) = 5(t² + 2t)⁴(2t)
• f'(t) = 5(t² + 2t)⁴(2t + 2)

Find the derivative of
 $y=\frac{x^2}{3x-1}$  

•  $y'=\frac{3x-1}{\left(3x-1\right)^2}$  

•  $y'=\frac{3x^2-2x}{\left(3x-1\right)^2}$  

•  $y'=\frac{2x}{3}$  

•  $y'=\frac{6x^2-8x}{\left(3x-1\right)^2}$