Finding Slopes of Tangent Lines

Find the fully simplified Derivative of y = 4x² + 3x + 6x^-2

• y' = 8x + 3 -12x^-3

• y' = 8x + 3 +12/x³

• y' = 8x + 3 -12/x³

• y' = 8x + 3 + 12/x

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

• m = 0

• f'(x) = -6x - 6

• f'(x) = 6x

• m = -12

Find f '(2)  if
f(x) = x² + 2x

• 2x + 2

• 6

• 12

• 2x

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

• y+1=2(x+1)

• y=2x-1

• y=2x+2

• y= -x-1

If f '(x) = 0, what does that mean with respect to the tangent line?

• Tangent line is vertical

• Tangent line has a positive slope

• Tangent line is horizontal

• Tangent line has a negative slope

Determine the equation of the tangent line for the following function at the given point:

Determine the average rate of change of the function over the given interval: f\left(x\right)=\frac{1}{x+2}; \left[2,\ 6\right]

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

• 6x

• 27

• 18

• 3x